If none of the suggestions in this thread help, at a shell prompt, do:

ipconfig /all

on the malfunctioning laptop, and do the same command on a functioning laptop. Locate the entry that describes the wireless adapter in each of those outputs and compare them to each other. The differences are likely to point the way towards the solution.

Most common problem is that the malfunctioning laptop doesn't get a DHCP address or a DNS server address.

Another common problem (already mentioned in this thread) is that sometimes, when you connect to a router with an incorrect wireless key, it acts like it's connected but simply doesn't work (doesn't give a DHCP address). You don't get the expected error that the key was wrong.