Hello and welcome to Tom's Hardware Forums.
If the computer won't turn on, one cause is the power supply unit which is the box inside the box where the mains electric cable plugs in. It's easy enough to replace - four screws hold it in and the cable connections inside, while looking confusing at first, can only be plugged in the right places and the right way round. A new one doesn't cost much - in Britain £25 will buy an average 450 or 500 Watt model. Prices in the states are always far lower than ours.