OK, first things first, use Super Anti-spyware to search and kill any adware, malware, spyware. Then use your virus checker to scan for viruses.
Second, can you try a new or another network card? I sometimes use a wireless dongle to test things - if same problem then you can rule out NIC or driver. Try a new cable (if using one).
Thirdly, switch off firewall and try again
Fourthly, switch off security (WEP WPA etc.) try again.
Fifth, can you test with a different router?
And if all that fails, does your firewall report anything similar to a SYN Flood Attack?
However there is one other thing you could try if you have the resources and skills to do it. Install Windows XP as a dual boot, boot into this and see if you get the same problem.
Let me know how these tests go.