I have a 2400 that turns itself off.  It is still in warranty.  haven't got it fixed yet.  Post if you get yours fixed and I will do the same.

Glenn

Hey guys. I too am having this problem with my dimension 8400 that i bought only a year ago. I have heard from many and believe that the problem is due to the power supply box. Either that or your computer is heating up, but i doubt thats the problem. Do you get a blinking amber light when you try turning on your computer....or when it shuts off does it blink amber??? if it does it may be the power supply box. I have called dell and requested a new one since im still in the warrenty and i heard doing this will solve the problem because the power supply box they send out to you is a newer one than the one currently installed. I'll reply and let you know if this helps my computer. Hopefully you can resolve your issue. Good luck.

I also have a Dimension 3000 that is turning itself off at random times. I have called tech support once and also have chatted with dell about 7 different times. They had us do diagnostic tests and it shut off while the test was running. We have already checked the power management settings and nothing. They have replaced the heat sink fan and the processor fan but other than that, it has not fixed the problem. I do have a question for you, when the computer shuts itself off. Does the green power light blink? If anyone knows of any solutions please let me know.

hey guys. I should be getting my new power supply box in by monday sept. 19, 05 so when i do ill let you know how my computer is working. Im almost positve thats what's causing the auto-shutoffs and restarts. The Current power box i have is an REV A00 but others who have had this problem usually get their power supply box replaced with a REV A04 (from dell)  which seems to work out fine for them. So I'll keep you updated and hopefully you can get your issues fixed as well. Good Luck.

UT Rocker

Well Guys my power supply box and motherboard both (finally) got replaced by dell and my computer hasnt shut off - yet. However, its only been 5hrs since it was fixed. lol. I'll post a comment in the coming days to let you know how the PC has worked. If you have any questions or comments concerning the random shutdowns or unexpected restarts, reply and Ill try and help you with what i can. Good Luck.

UT Rocker