Garage door opener won't close door

I tried this one over in the Home Repairs forum but it's been a while and no response so I figured I'd try here instead. My garage door opener is not working properly--it will open the door just fine but once it's open it won't close (it doesn't even start to close--just sits there and does nothing). It does it whether I'm using the remote or the button on the wall (both work to open the door, neither works to close it). For a while it would sometimes close and sometimes it wouldn't, but now it won't close at all. It's an older unit but I can't afford to replace it right now so I'm hoping it's something that I can fix to make it last for at least another 6 months or so. Any ideas what might be wrong with it?