Warning: random train of thought follows.

Something specific about XP? Hm.

The problem with the wireless, for instance, might be that XP doesn't, by default, speak the newer WiFi security protocols. If that's the problem, there are downloads to help you out:
http://www.microsoft.com/en-us/download/details.aspx?id=3914
http://www.microsoft.com/en-us/download/details.aspx?id=1974
... but that's just a wild guess.

Wired... I don't know what the issue is there without a hands-on look a the thing.

Hm. Now that I think about it some more...

The fact that you have the same problem with both wired and wireless, indicates to me that the problem is in the configuration of your router. First guess is that there's something wrong in the routing table, and it's messing things up just for *that* computer's MAC address. I wonder if, on one of the interfaces, you could spoof the MAC address to something different to force the router to think it's a different device.

Well, anyway, the first base diagnostic steps are to go into the TCP/IP properties/configurations of the Wireless and Wired interfaces, and make sure everything is set to the defaults, i.e., "automatic" for all the TCP settings. In other words, no hard-coded Gateway IP address, or DNS settings for example.

If all that looks good, force a DHCP refresh:
IPCONFIG /RELEASE
IPCONFIG /RENEW
IPCONFIG /FLUSHDNS

If that doesn't fix it, try to narrow down whether the problem is a DNS issue or a TCP routing issue. Do it like this:
- On a *working* computer, ping www.google.com and see what IP address it gives you.
- On the non-working computer, ping *the IP address directly*, not the name.

If the IP address works, then your issue is entirely DNS-related, and your network interface and routing is fine. Start looking for reasons that DNS might be malfunctioning.

Other things to try:

The fact that it worked when it moved to the computer repair guy's network means it's something about YOUR network. When you tried plugging it into the cable modem, is EVERYTHING ELSE on that network turned off and/or disconnected from the cable modem? For instance, maybe the bad computer has the same IP address assigned as one of the good computers that's already on the network, and so the good computer is already up and running on the network so the bad computer can't work.

Hm. What if this computer had Internet Connection Sharing turned on, and it only active when it's at your house?