Keeps shutting down and rebooting. I have checked

It is probably the powersupply although Dell is right and it might be a motherboard problem. Your best options right now are to replace the power supply first, then run a motherboard error check if you have an adapter for it. If you don't you should take it in to a repair shop unless it's still under warrenty then Dell should be able to fix it for you. If they try to charge you alot of money, call around and see if you can't get a better deal first because sometimes factory warrentys don't amount to anything more than a headache.