If the children who used it were the knowledgable type, there could be problems with the BIOS or CMOS (ie: they tried to overclock it or something). Resetting the CMOS jumper (following the instructions in the manual) may help.

Also, I've had machines fail to POST (power on self test; the first beep you hear) because the memory wasn't pressed in all the way. After installing RAM, I give it a firm press on the center of the thin edge, making sure it's in.

If all else fails, blame it on bad IDE headers and send it for repair.