It would appear that I am dealing with a computer that is working contrary to the widely accepted notion that wired connections are more reliable than wireless ones.
The computer is normally connects to the network wireless using a Belkin Adapter. No problems there. However I needed to hardwire it to the network for work purposes and so I plugged in the cat5e to the router and then to the computer, and of course disabled the wireless adapter. And there the problem starts, because the Ethernet adapter is stuck on "Acquiring Network Address". And even when it's saying that I open up a browser and it sees the homepage, but if I move away to say google, I get an error in connection from then on.
I've tried repairing the connection through the Windows networking feature, and also using the prompt to release and renew (which doesn't work because it says that "no adapter is in the state permissible for this operation"), flush and register the dns cache, which seems to work fine, and I was also having a problem with clearing the ARP cache before, but I solved that by disabling and stopping the Routing and Remote Services, well service, through 'services.msc'.
Sorry it's a bit long, but I'm now down to just wondering whether or not it's a problem with the driver for the ethernet adapter (it's a Broadcom NetXtreme Gigabit adapter). I've already tried to update the driver, but Windows says it cannot find a better driver for it.
Oh and I have also tried the ethernet cable with more than one machine, and it works fine with those, so that's not the problem either. Any and all help is much appreciated with this strange behaviour.