Point to point testing at what level?
Do you mean with your cable tester (which is mainly the physical level)?
Or perhaps the ethernet level (layer 2)? Perhaps best seen by the LEDs associated with each port lighting up (though I'm guessing at that)
Or perhaps it is working just above the ethernet level - so perhaps the ARP protocol works?
Or perhaps is is working at layer 3 - where ICMP pings work successfully.
I suspect you mean your cable tester alone.
I can't help but think that your testing starts with a layer 1 test, and then jumps to assume that all the intermediate layers are working, before concluding that access to the internet is not working - by running an application at layer 7.
I think you need to start checking the lower layers of the LAN before worrying about routing out onto the WAN.
As you've jumped to having large ethernet switches, you've probably outgrown any home or SOHO solutions. The switches you have might, for example, have included VLAN functionality, where not all ports are meant to be switchable to all other ports. Or perhaps the auto-negotiation for 10/100 speeds and half/full duplex has not worked.
Or perhaps you are hitting a problem with the switch as you move your laptop from port to port - that it remembers your MAC address wrongly, and directs traffic down to an old port.
Perhaps you are relying on a faulty DHCP server at the IP layer, and the PC isn't being given an IP address properly. Perhaps this is interacting badly with ARP caching in the switch.
I suspect that you will need to check the intermediate layers with ARP and PING commands, while keeping a fixed IP address for the PC. You might even need a second PC.