Can you give us details about your mom's network setup? Like, whether the PC is connected directly to a modem or whether there is a router box.
Following the cables that go out the PC's back is a good way to find out, you certainly can identify power supplies, sound boxes, monitors and printers. Following only ethernet cables, should you know how they look, helps. Anything not on that list is probably either a modem, a router, or a switch. Or several of those things combined. It must have a product name printed on it, please post it here.
(like gnorty says) If your mom is running Windows XP, there is also the chance that the build in firewall, or in fact any personal firewall software that is running, is blocking access. So you should find out whether a firewall is running and have a look at its settings. Post the software's name here, perhaps someone is familiar with it and can help you get around.
But first, can give us your IP adress?
http://www.whatismyip.com/ tells you what it is. We can then check the master log files whether the problem is that incoming or outgoing packets are blocked or lost.