Computer won't come on without beep

My niece says her computer will not always start after turning it off.
She says sometimes when she turns it on, the computer will not beep
and does not start. When she tries again and the computer beeps, it
will start.

I went to see them yesterday. I opened it up and made sure the memory
was seated and the power supply wires were plugged in. She said that
it still does it occasionally.

What else could be causing this?

--
O'Neil to General Hammond:
For the record Sir, I wanted to blow it the hell up.