It turns on, stays on for about 10 seconds and

The lamp is the most likely problem, check that first. There is an lap door you open by taking out one screw and then inspect the lamp for a cloud near the stem of the bulb. If it is cloudy, most likely you lamp is going out. If the lamp is fine, the ballast is going to be the problem that is failing to sustain arch for the lamp.

Just replace the lamp. It will then work like new. It's very simple, taking just minutes.