I would say use the search function first. All your issues start with bad capacitors. The sound on the classic is on the analog board, and if those are bad I am sure the motherboard needs recapped also.

To the question is it worth it? Well that depends on you. All the caps for the analog board and motherboard could be around 40 dollars after shipping, then if you cant do that yourself then you would have to pay for that. I need to recap my classic and classic II analog boards, I have not yet because I have so many projects but to me I think its worth it.