I've had that happen on a couple of old computers, my first instinct with random reboots is always the motherboard, then it goes to power supply, and if the computer is really old the third is dust. Of course viruses and spyware can also wreak havoc on computers.
I'm typing this from my MacBook Pro which is by far more user friendly than any PC I have ever used. The only problem I had with it was a faulty battery which is a known problem with these things. I actively try and recruit anyone who isnt an avid gamer to the mac side anytime I can, so I say tell em to get an iMac!