fluorscent light, two bulb 8 feet long.
I agree with Joed. The ballast would be fairly simple to replace IF you can find the correct replacement. Be aware that there are TONS of configurations for ballasts - you need to make sure you get one that is for the correct T style of bulb (thickness of bulb = t8, t12, etc), as well as length (2 - 4 - 8 feet), as well as number of bulbs per fixture (single, double, triple, quad, etc). You should also try to get the same type of ballast (analog (old) vs electronic (new)) as the wiring may be a bit different on different types of ballasts.
If you can find a ballast that has all the same specs as your current ballast, changing would be as simple as opening the fixture, undoing a few wire nuts (document what colors went where), unscrewing old ballast, putting new ballast in, and putting wire nuts back together.
Finding the correct ballast is going to be your biggest obstacle - if you don't think you're up to it, replacing the entire fixture with a new unit might be easier. The new unit will likely come with an electronic ballast which SHOULD have a better service life.