I need a program that I can use to connect to my parents desktop/laptop and control the computer. Or at least be able to see the desktop to see exactly what is happening. I thought about VNC but I seem to remember someone giving me a reason why I wouldn't be able to use it. Their PC and laptop are networked together through a router, if it matters.

use xp remote part of the xp pro package
to remote to other ms os
remote client
or radmin not bad have not used it much since I went kvm

You can use any remote control software.. RDP is built into Windows, Radmin is really nice (but you have to pay). Maybe you were discouraged from using VNC because the vanilla version doesn't support encryption? UltraVNC has encryption and also supports chat with users and file transfers.

You will have to set up port forwarding on the router and open the relevant ports in any software firewalls.