Why not try fixing it? It could very well be something extremely simple. Here are some possibilities:
1) Bad jack: It's supposed to cut out the internal speaker(s) automatically when a plug is inserted. If the contacts get flaky, one or more channels might disappear on occasion.
2) Bad capacitor(s): As you noted, this could be a problem. Caps are cheap, so there's no harm in simply replacing 'em. Certainly replace any that are leaking/have leaked, and any that exhibit noticeable bulging at the top. The audio capacitors will generally be located near the speaker connector (although I don't know about the IIci for certain), and have relatively high capacitance values (e.g., 100uF or more).
3) Control panel setting: If the balance slider is set to one extreme, you'll only hear one channel.
This is hardly an exhaustive list, but it covers several common sources of the problem you're seeing. You can tell that the fixes are easy and inexpensive, so you may want to consider trying those first.
Others will shortly contribute their suggestions as well, I'm sure.
Good luck!