Not good!
The first suspect is the PSU may be faulty. The best way to test that is to replace the PSU with another working PSU. The replacement PSU can just be another unit at hand, or a unit borrowed from a friend/neighbor etc. This will either confirm or eliminate the original PSU as being faulty.
So. With the replacement PSU installed, if the computer starts up and runs fine, then the original PSU is faulty and should be repaired or replaced. If the computer still doesn't start up, then the motherboard may be faulty. Try the following test procedures as well.
Try using only one DIMM, and if necessary try moving to other slots. If computer still doesn't start/run, then try other DIMM's (at hand or borrow them).
If computer still...