Multitude of issues...

Problem 1:
Your laptop might be overheating. Try getting a cooling pad of some sort, and take a good can of compressed air to it would be my first suggestions. Also try checking your Event Log, under Control Panel > Administrative Tools > Event Viewer, and the System and Application tabs. If you see any red-x errors, check them out.

I'd also recommend a running of some anti-malware program like Spybot Search & Destroy to see if it picks anything up, if you've not done so already.

Problem 2:
First, what's the model of the router, if you know?
Second, what's the actual error that gets spat out? If it's something like "IP Address already in use", follow the below--if not, ignore it and skip to problem 3's section.

Are both computers that try to connect set up with a static IP? If they are, that's your problem. IE, if both computers try to connect as 192.168.1.100, one will fail. Go into your Network Connections applet in the control panel, and on the appropriate connection, hit Properties.

From there, scroll down to "Internet Protocol (TCP/IP)", and hit properties on that. Make sure that Obtain IP address automatically and Obtain DNS servers automatically are both selected (the "Use the following" options not selected, basically).

Once that's done on both machines, disconnect them, and reconnect (or reboot, to be sure). See if that helps?

Problem 3:
Download and run CCleaner on her system. Have it fix everything it finds on both Application and Registry tabs. Or, to not go the instantly (possibly) destructive route, run Hijack this!, and post the logfile it produces back to this topic.

Someone will be able to take a look at it and give you more help.

Jam it back in, in the dark.