MY 95 Neon has a constant ooo/humming noise when I turn on the engine and gets louder after the car warms up?

MY 95 Neon has a constant moderately high pitched (about an octave above middle C) ooo/humming noise when I turn on the engine and gets louder after the car warms up. This noise has a constant pitch and stops when the engine is turned off. It does not change witht he RPM or gear or car speed. It is relentlessly driving me nuts. Is it the fuel pump? radiator/water pump? I had the belts checked and the guy said they are OK. He didn't seem to hear the noise because the car was not warmed up yet (It was there but he couldn't distinguish it).