I had wondered about capacitor issues with older compact mac models, and it appears that SMT electrolytic capacitors are not used for them. But there are some electrolytic capacitors present so if you have the ability to test them, that could be one area to look. If there is no gunk leaking out anywhere, I would be surprised if a board cleaning would actually help... but it most likely wouldn't hurt the board either.
If you don't get advice that pinpoints the exact component given these symptoms....I agree intense visual scrutiny is a good start to see if anything has "burned up". If you can take well-light high-res shots of the board and post, there are more eyes available here to help.