Not worried about the repair, soldering in a new cap is no big deal (done that plenty of times and doesn't require an electrical engineering degree). You're quite right about figuring out what caused it, except caps being what they are, it is all but guaranteed just to be normal wear. Caps tend to be the first thing to go on any electronics, and this is a 6 yo rental unit. It has been used alot.
That said, looking at prices on new units, barely looks worth teh effort to repair the old one! May just do it that way.
3 months in a Sunseeker touring ski resorts: TheSkiDream.com