|Unplug the case/power supply.|
Power off your monitor.
Open up the case by removing the left panel as seen when you're looking at the front of the case.
A common thing that can happen with ram, even ram that worked fine previously, is the ram has, or has developed, a poor connection in it's slot(s).
This usually happens a long time after the ram was installed, but it can happen with new ram, or after moving the computer case from one place to another, and I've had even new modules that needed to have their contacts cleaned.
See response 2 in this - try cleaning the contacts on the ram modules, and making sure the modules are properly seated:
If doing just that doesn't help...
It's extremely rare for ram that worked fine previously to spontaneosuly go "bad", and even more unlikely for more than one module to go "bad" at the same time, but if ram that is incompatible with the mboard chipset or the cpu has been installed, memory errors will likely occur, and in the worst cases the computer will not boot, and the mboard may not beep at all.
Did anyone change which ram is installed since the last time the computer worked properly?
Check all the connections of the wiring to make sure they are all the way onto their pins and into their sockets, especially the main connector from the power supply. The wires close to the mboard going into the main power connector/socket should be more or less perpendicular to the mboard surface rather than at an angle. Make sure all cards in slots are all the way down in their slots.
While you're in there, if the cpu fan/heatsink has mung (dust, lint, etc.) on it, clean it off, but DO NOT use a vaccuum cleaner to do that (they produce a tremendous amount of static electricity when running, and anything connected to them can discharge that to your components) - use canned air, or an air nozzle if you have access to an air compressor, or an artist's brush that can be used in small spaces, etc. It may be difficult to clean the top of the heatsink under the cpu fan - the most likely place to have mung on it - and the bottom side of the cpu fan blades unless you remove the fan. If you have a case fan, clean that too if it needs it.
If you have a video card installed in a mboard slot, if that has a fan and heat sink on it, check that for mung too.
Check the power supply openings for mung too.
With the cover still off, restore the AC power, start the computer and make sure the cpu fan spins - if it doesn't spin, if you're sure the power supply is working okay, don't use the computer until you have replaced it.
If it spins too slowly, and/or if it makes rattling or screeching noises, most likely to be noticed when the computer has cooled to room temp, has not been used for a while, and then is started up, the cpu fan's bearings are failing - replace it as soon as you can.