Latitude 100L Crashes if power cable is attached

A friend has just asked me to fix their latitude 100L which is suffering from a rather obscure problem. When you boot it up with the power cable attached it hangs before it gets to the BIOS screen. All that is visible is a flashing cursor in the top left hand corner.
However if the power cable isn't attached and you connected during boot up wherever it is in the process it hangs immediately.
Finally if you don't attach the cable at all and leave it to boot it will reach the screen with the XP logo and most often hand there, occasionally loading windows, if windows does load however it usually blue screens within minutes.
One thing I did notice is after charging it last night then leaving it unplugged overnight then trying it this morning without the power cable attached it seemed to load windows and work to an almost acceptable degree.
I've tried some boot disks to back up the hard drive over my network but I can't seem to get them to find my shared documents. I've also done a hard disk scan from within one of these disks and there seems to be no problems with the disk.
I can get into safe mode but once there I don't really know what to do.
Any advice would be appreciated at this point.