If there is anyone who owns a Dell m1330 and has a problem with it randomly restarting and/or showing random coloured vertical bars on start up, you are not alone. It happened to me as well as many others. There is a thread about this problem over at Notebook Review Forum that is (currently) 30 pages long!
There is only one solution for this problem: a motherboard replacement. This problem seems to only occur with those that ordered their laptop with the nVidia GeForce 8400GS. This graphics card is actually a chip that comes as part of the motherboard, and the most likely explanation for the problem is that it just produces too much heat, effectively frying the motherboard.

Upon calling Dell about this problem they will ask you to upgrade graphics drivers, upgrade bios, do a PC Restore/factory image/OS reinstall. Trust me, NON OF IT WORKS. It did not work for anyone else with the problem and it did not work for me. Either tell Dell you know it is a hardware problem, or lie to them and tell them you already did the aforementioned. The support staff does not know any better anyways.

I had my motherboard replaced today and it fixed the problem. If you do not have a three year warranty I would suggest trying to get one. Apprently the latest revisision of the motherboard (A04) has not yet solved the issue. Not only that, it is likely that your board will be replaced with a refurbished A00 or A01 board, meaning that there is a good possibility that this could be a recurring problem for quite some time.

Regards,
Chris