I bought this thing second hand last summer. It did this before, but then stopped and worked normally for close to a year. Now it won't finish a cycle. It fills, agitates for a short time, then sits there. It drains when we take out the hose. Should I just buy a new one, or is there hope?

It might be a bad lid switch.
Check out this link for more info.

Another possibility (especially since it drains when you take the drain hose out) is that the pump is not turning. This is more work to get to, but make sure that there is a belt going to the pump and that the pump itself can turn.

Best of luck,
WallyH