Check the cabling, reboot router, reboot PC, if that doesn't work open up a command prompt:
type:
ipconfig/release
ipconfig/renew
It should pick a new one up, then try pinging google. If it still doesn't pick up a valid IP you have a problem either with the hardware on your PC or the connection to your DHCP server (probably the router) however as your other PC is working I'd hazard a guess that it'd be your PC. Possibly reseating cabling, checking you're getting lights on the network card when it's plugged in etc.
ping www.google.com
If you can't ping google it's possibly a DNS issue, try tracerouting it:
tracert www.google.com
It should look something like this:
Tracing route to
www.l.google.com [173.194.78.105]
over a maximum of 30 hops:
1 47 ms 100 ms 99 ms (removed for privacy)
2 14 ms 14 ms 13 ms (removed for privacy)
3 15 ms 15 ms 14 ms (removed for privacy)
4 22 ms 22 ms 23 ms (removed for privacy)
5 22 ms 22 ms 22 ms (removed for privacy)
6 22 ms 22 ms 21 ms (removed for privacy)
7 22 ms 21 ms 22 ms acc1-10GigE-0-3-0.mr.21cn-ipp.bt.net [109.159.250.82]
8 32 ms 35 ms 36 ms core1-te0-4-0-0.ealing.ukcore.bt.net [109.159.250.1]
9 59 ms 85 ms 30 ms peer1-xe1-0-0.telehouse.ukcore.bt.net [109.159.254.98]
10 28 ms 29 ms 30 ms 195.99.126.113
11 30 ms 40 ms 28 ms 209.85.252.186
12 29 ms 30 ms 29 ms 209.85.253.90
13 35 ms 36 ms 35 ms 66.249.95.173
14 35 ms 35 ms 35 ms 209.85.251.231
15 * * * Request timed out.
16 36 ms 36 ms 36 ms wg-in-f105.1e100.net [173.194.78.105]
Trace complete.
If there is a DNS issue it'll fail to translate the
www.google.com into a valid IP address and tell you. If it does and the traceroute ends without hitting
www.google.com you have a routing issue.
I'd be surprised if it was a routing issue as the other PC seems fine, however it could be the router isn't issuing IP addresses, the cabling is faulty, your PC has maleware on it or you've statically assigned network settings which aren't valid for your current network (invalid IP, wrong subnet etc).