The laptop can see and connect to my desktop computer which is running win7 pro x64, but it cannot connect to another computer on the network running windows xp pro x86 by typing it's name. The laptop can however connect to the xp computer if it types in the ip address of the xp computer.-nite_monkey
If it can connect by IP, it can connect. So fiddling with SSIDs, sharing permissions, & etc. is probably just a good way to break something else.

Ping the IP, I'm guessing you can.
Ping the Name, I'm guessing you can't
Make sure that NetBIOS name resolution is enabled on all the relevent adapters, because this is a NetBIOS name resolution issue.
It could be a fight over who is the Browse Master, or it might just not be anouncing itself correctly. This is a big part of why I hate working on WorkGroup networks; XP is prone to pull this crap, and I never did find a clear cut method of troubleshooting it.