I think you hit it here:
"The NAS drive is working in such a way that it is creating a massive overhead on the switch inside the router and as a result the router does not have the processor power for the other connections?"
The op needs to get a switch (1000mbps) and plis this into the router and then all pc's, mas drives into the switch also. [[b]Router <=> Switch <=> PC's/Nas etc]
Yes, this is never a bad idea in any sort of enthusiast home network.
I'd agree about using a separate switch as soon as there are more than a few devices on the network and/or if thinking about having multiple internet connections or changing the router, just as it keeps the LAN side of things operational rather than depending on the thing providing the internet connection.
The original comment about the overhead on the router internal switch is a bit of a red herring, Even on consumer routers, that is a hardware switch chip and the router CPU isn't used for data flowing between the switch ports.
(The switch is programmed during boot up so it still needs a functional CPU at that stage)
That still leaves the possibility that the NAS is either misconfigured (network settings) and/or is hammering the internet connection (either in bandwidth terms or opening too many connections) for example if it has a queue of things it can download itself, a torrent client or is trying to sync with a cloud storage service.
I expect a well-behaved NAS will have settings that can limit the amount of bandwidth / connections it uses on the so as not to gum up an internet connection.
prompt $P - Invalid drive specification - Abort, Retry, Fail? $G
prlzx on iDNET: ADSL2+ / 21CN at ~4Mbps / 700kbps with IP4/6