Hi,
I bought an iBook G4 from ebay. It's my first apple so when it repeatedly reported "You must restart your computer" usually prior to the login screen although sometimes it went past the login and stayed workin for about five minutes before it happened. I thought I'd bought a duff one and wasn't impressed. After several hours of searching the web and trying various solutions (including following a video on youtube about taking it apart and placing a piece of paper over one of the components - which in this instance didn't help). I eventually came across a post [can't remember where] which said that you could find out what had caused the panic by looking at the panic log, this should be found at /library/logs/panic.log.
After rebooting several times to get far enough before a panic occured to read the log I finally managed it. In the log I found that every panic entry that had been reported contained details relating to AirPort. Other post on the web also mentioned that the Airport card is sometimes know to cause panic problems. I disabled AirPort by clicking on the Airport icon at the top of the screen and the problem did not occur. The upside is the problem has now gone completely, the downside is that I had to buy a USB wireless adapter but it only cost £10.
I would definately suggest looking in the panic log before doing anything else. At least if the Airport card is causing the problem this is a pretty cheap way of sorting it out.
PS. We accidently switched on the Airport a week later and the panics happened almost immediately and continuously

. Needless to say it got switched off for good after that.
Regards,
Lee