Okay - used arp -a in CMD.exe and all I got was "No ARP Entries Found."
I tried pinging my router and it just says "Destination Host Unreachable."
Did both with a laptop and got entries as normal.
What really confounds me is that the Wireless Network Connection says it's connected - but only if I boot the computer and have the home network as an autoconnect. If I disconnect and attempt to re-connect, it refuses.
Thanks for your help, BTW.