This is aimed at desktop/tower machines, if you are fighting a laptop probably only 1) and 2) below are possible, and maybe 4).
Try these in the given order:
1) Remove then re-install each RAM memory board
2) To get to the BIOS setup, repeatedly press the F2 key immediately after power-on. From there you may be able to determine which memory board is giving trouble. (If you get here and the BIOS settings look wacky, the CMOS Battery is a prime suspect. {You may need a Dell expert to define 'wacky' though.

})
3) Repeat the remove-reinstall dance with any expansion cards in the machine and see if there is any progress.
4) If you can't get to the BIOS setup, a computer will often function enough for keyboard access to the BIOS with just one memory board installed, usually the one closest to the CPU on the motherboard. If there is more than one memory board, try installing one board in the first slot only and see if you make any progress. If not, try again with a different memory board in the first slot.
Another common failure is the Power Supply, which can give all sorts of weird symptoms. In desktop/tower machines, they start to become a suspect after about 5 years of age. (Takes more than hobbyist equipment to test them. Swapping in a known good one is the best route.)
Tha above are only the first, most common, steps in finding the problem. Beyond these the number of possibilities explodes, which generally means "Find someone with experience you can rope into help." I see on your profile page you are working towards a PhD, if you attend an instructional institution there are probably tech support facilities of some sort available.
Good Luck, and keep us posted on your progress.
Cheers,
Tom