Does computer A have any files shared out over the network for computer B to see?

I really don't know about this, please tell how to check that?

This sort of depends on whether you are using XP Home or Pro. Generally, both setup a "Workgroup" XP Pro does so by default, XP Home can be hit or miss. Assuming that you have the default Workgroup set up, and assuming that if XP Home is defaulted to Simple file sharing, bring up Windows Explorer. It generally defaults to My Documents, click on the "+" next to My Computer and then click on the "+" next to C local drive. Generally under Documents and settings, you will see a folder called Shared Documents. Actually, you can create your own Folder if you like. If you find a Shared Documents folder with a little hand beside it, it means that that folder will be seen by any computer on your network. If there is no little hand, then right click on the folder and choose Sharing and Security from the menu. If you are using XP Home don't use the Wizard since Microsoft wants to turn on the Firewall which is a real headache when you are first learning to do this. Filling in the blanks are pretty straight forward.

I have the same problem. Two computers connected via wireless router. Both definitely have the same workgroup name and both have a shared folder. I am unable to even ping one computer from the other, though. I get a timeout.
 
Any other ideas? Thanks in advance for any suggestions.

If you are running any kind of firewall (software like norton internet security or hardware on your router), add the ip addresses of the two pcs as 'trusted addresses'. norton internet security definately wants that. hope to have helped