The is a mainboard failure --  the system board will need to be replaced (or given the age of the system, since that is likely not an economically sensible repair, the system needs to be replaced).

Thanks for replying, I was wondering if flashing the new bios would fix this problem? If not I guess I'll begin looking for a new computer.

At powerup, press F12 a few times.  If the system will load the diagnostics from the menu, run an extended test on the storage drive and memory.

If the system won't even run the diagnostics, it's time for either a replacement mainboard or system.

What is the exact system model? What is the current OS installed on the system?

When did the issue start? Is there any damage on the system?

Update the BIOS - http://dell.to/1n3X2po  - enter the service tag and download the BIOS, update and restart the machine and check.

Restart the system and press f12 key on startup - choose diagnostics. Let it run the diags and if you encounter any errors - make a note of the complete error and report the same to us. These are onboard diagnostics and they might possible pick some error if the hardware is not functional. Also, run an extended / thorough tests on the HDD and memory to check for any possible errors. 

Restart the system and check in safe mode - http://bit.ly/1LHcO2c

Enable the built in admin account and check - http://bit.ly/1JoFhcw - This will help isolate if the issue is profile related or not.