I have seen a similar symptom a couple of times, where it turned out to be the RAM contacts to the MOBO.
she could try removing the ram and re-installing it(WHILE the power is OFF),
but also have seen the symptoms with a power supply on the way out, and depending upon the rated power of the supply and the specs of the computer it might be near the end of life, and the replacement of the supply fixed the problem.
hope one of these suggestions help
harpo