I have a Klipsch 10'' sub that pretty much stopped working one day. one day it was playing, the next day it would just "mumble". I thought I would do that same thing, look inside and try and find burnt, broken, or obvious signs of trauma. I took the amplifier plate off the back as my point of entry. it comes off easy enough. But, unless there's obvious signs of trauma, I don't know that you will learn much. As lovinthehd said, looking at the driver itself may tell you more.
In my case I got a price from a local repair shop and then a price from Klipsch to replace the amp. It was not a price performer to repair it since the Klipsch sub really isn't a very good sub to begin with. So, I didn't repair it but saved up some shekels and bought a really great sub. But, looking inside is definitely worth the effort. I found it interesting and informative.