This is a big post - summary at the very bottom !!!
Quickest and cheapest worthwhile check is a new cable - except we need to be *very* careful on terminology to avoid confusion. Specifically, you need to make sure you check with a new, or known-good, *ethernet* cable. Preferably a fully-wired 8-conductor one.
Some cheap "ethernet" cables are only 4-wires inside 8-pin plugs, typically supplied with older cheap CPE (ISP-supplied routers) Avoid them uness you are absolutely desperate and have nothing else.
Reasoning: this above assumes that you have only been checking with one ethernet cable and that it might be faulty - hence trying a new one. Costs very little and you may have one lying around
Personally, I'd also try a new power supply: match the voltage ("V") exactly, connector too, and a current ("amps" or "A") equal or higher to the original.
Reasoning: a failing power supply is a nightmare. It can cause all sorts of obvious faults. Worse, it can cause a lot of confusion and irrational behavour but only under certaion conditions. For example, it may just be able to run the router OK most of the time when used only for wifi, maybe fine on on a cool day, until the extra load on the voltage rails from the ethernet transceiver when you plug a cable in- this is in the region of only about a few tens of milliamperes maximum per port but I've seen this happen once before. It's not very likely though. Sometimes it's the other way on - ethernet ports work OK but when wifi is under heavy load it'll cause a problem. There will be several power supply rails for various things insude the router, each one could be affected by a bad external PSU in complex ways, independently or in combination. Nightmare.
Often in a case light this the router is rebooting or glitching and it's hard to know what's going on. The specific methodical process listed below can help you identify this.
Ask yourself: has the unit been running warm of had bad airflow around it? For example,. sitting on a carpet is much worse than on a flat, hard surface like a table. Did you remove and plastic protection sheets that it mah have arrived with? Removing them allows a little more heat dissipation. Could it be in an area of warmer air? For example, above a radiator,
Reasoning: longterm heat damage can manifest in various ways. I notice this router modelhas a ceramic heatsink on the XWAY IC, so I assume it's a warmer one than some routers that don't need one. If it's heat damage, then you need a new router unless you fancy doing compnent level repair and have very good soldering skills. Not worth starting to repair it unless you are already a well-stocked electronics repair person with the gear and skills. To pay someone for such a repair is usually uneconomical too, you just by a new router if you have to.
Here's what I do, to simplify the confusion possibilities and speed faultfinding. This is a generic workflow for this type of symptom, not specific to TP-Link :-
1 Router on a table in front of you where you can see it, nothing plugged into it - no cables at all, not even the power. Slow down your thoughts and watch for clues as you proceed. One thing at a time, in order...
2 Plug in new or known-good ethernet cable, other end to known-good PC that is running (if you don't have a PC, at the very least least use something like a switch, AP or second router that will show you a link state LED so you know the cable is OK once tyhe router is booted, read on)
3 To clarify the above that means *no other cables yet*, none to phone line for example - to keep it simple. We don't even have the power supply lead in, because we watch things as it starts up.
4 Only now insert power supply and connect mains to router.
5 Watch router LEDs - it'll be going through a bootup sequence - exact meaning of lights is not really important - after the lights settle down, you should see the appropriate ethernet port link-state LED lit.
With a router that is not connected to the phone line at all, there should be a quick-ish boot, maybe 10-40 or 50 seconds, then it should "settle down" LED-wise. Exactly what you should see during the bootup stage in not important, when it settles, it'll be obvious that it's finished the bootup, so you can look for the all-important link-state LED.
This LED, for your appropriate ethernet port, should be constantly lit or nearly so (occasional flashing or flickering is normal especially if there traffic on the wire, but you need much more on that off. Technically, we'd say a 90% duty cycle or higher on-state of the LED is good, off is bad, and a 50/50 one off is also bad.
6 If not, move the ethernet cable to another port. Observe that port status LED.
No joy? Try the other ports, one at a time.
7 Access router web config pages -
look for a router uptime, hopefully you can see it somewhere (that's the system uptime, not any DSL connection uptime - we have no DSL/phone cable in remember, deliberately.
Make a note of the time on your watch. Have a cuppa. Come back, make sure router has not spontaneously rebooted in the meantime. If it has, uptime will not match so, try a different PSU if you have one handy
...Assuming it seems to work OK for say 10-15 minutes (this allows unit to warm up, thermal faults can cause spontaneous problems but it may run OK from cold for a while - often a bad electrolytic or dry joint)...
8 plug phone line (VDSL/ADSL cable into wall socket - observing router LEDs.
..at this stage, I'd watch to make sure the router doesn't reboot *itself*
9 a DSL connection may or may not occur, after a delay at this stage - most routers will sync and forward after a minute or two at most from an already-booted state. Some may need a reboot to sync, by design or bug.
10 If it seems to work OK, allow a futher 30 mins to warm up - check it again - uptime OK, is DSL sync sill connected. Does it work OK? If all is well, great. If not, borrow a matching PSU before you fork out cash for one if at all possible.
11 finally, to *prove* normal functioning in a commercial environment. I'd insert a (blank) USB flash stick in each USB port of that router and allow an hour or two for temperatures to stabilise. (Even better, a 200-300mA resistive load, be it 3.3v or 5v at the USB ports (yes, that's not a typo) The extra draw of the flash drives will load the internal power rails a little more and give you more confidence the router is stable. or not

I'd also connect all 4 cables to a switch or other PCs and use the wifi (both bands, if possible, passing lots of traffic (huge video files) back and forth so you really work the system, preferably while connected to a VPN oif the router has that capability - this works the CPU hard. I'd leave it "on soak test" overnight if possible as a minimum.
3 years is
plenty time for a PSU to go bad or certain router components to degrade, especially in a warm place. You can't reverse heat-related aging easily. In nice cool environment, say under 18degC you can sometimes get 3 to 5 or 6 years from a quality PSU and consumer router. At 14 or 15 degrees year-round you may get 8-10 years. . At 20-22 degrees, 3 years is more like it. At 25C, 24 months, at 30C 12months or less.
Often it's just the PSU, so always attempt to borrow one to test before you commit to buying a whole new router. If you have kept the router itself cool, a new PSU can be a good investment.
TP-Link is good quality for the price in my book, so look after it by keeping it cool or at least prevent it overheating. Just use common sense - you don't need fnacy heatsinks or fans in 99% of domestic cases.
Barring physicaly damage or a nearby lightning strike, bad PSUs and heat from poor location/ventilation are what cause the most problems that I see.
Bear in mind that intermittent faults or confusing faults are a real nightmare, hence the simplified, one thing at a time process above. Sure you could get all gung-ho and just plug everything in and watch it not work for hours on end while you go insane. It's up to you. I went insane decades ago, I'm just trying to ease your pain a little
.
PSUs can read fine on a DC voltmeter, even under load, but can go bad in ways that they produce excess ripple or noise that a simple meter doesn't measure. There are ways of measuring this, but life is too short - just swap out a PSU if you can.
oh - not all routers have system uptime on the status page, so you may need to use the
log instead and do a little detective work.
TL;DR summary:
New Ethernet cable is cheapest and often you have a spare. Try that first
Nojoy? Try a new PSU if you can borrow one. Common problem at that age.
Methodical process above will prove a problem or eventually inspire confidence.
Spend money only when you are SURE what the problem is.
Keep stuff cool and well ventilated for long life.
PSUs can go bad for various reasons, not just due to heat.