Why is my desktop PC unable to get an IP Address from the router?

The following Microsoft Support articles treat the repair of TCP/IP and Winsock :

How to reset Internet Protocol (TCP/IP)

How to determine and to recover from Winsock2 corruption in Windows Server 2003, in Windows XP, and in Windows Vista

In a nutshell, as administrator you should enter in a command prompt:

Reset TCP/IP

netsh int ip reset c:\resetlog.txt

Reset Winsock

netsh winsock reset

Can you open a command prompt and type ipconfig /release and if no error then type ipconfig /renew, what response do you get?

Check the router to make sure there are available IP addresses. If the DHCP range is small and the lease is long, the available IPs can all be assigned.

Finally, you can try manually assigning an IP you know is unused in the same subnet and trying to access the web.

Could be that windows update installed a new driver for your network card that isn't working. Check the date on the network card driver (My Computer-> Properties -> Hardware -> Device Manger) If the date is very recent date you might try rolling back the driver.