A device you are willing otherwise to recycle is the definition of "no courage required"; it's not a multimillion dollar mainframe you might damage.
Should you attempt the task and fail, all you could possibly suffer is a few $ wasted parts (probably less than 10), and possibly a popped circuit breaker and snootful of magic smoke, worst case. and it might work.
Not all bad caps are necessarily visually identifiable, but most of the time, bad caps are indeed the culprit; consumer goods usually use cheap, shoddy ones. So open it up, write a list of all the values and voltages of the electrolytics, place an order for replacements (I like
mouser.com, but
digikey.com is a possibility as well), choose LOW ESR for all of them, try swapping them out. You have better than 50/50 chance of success, and it's a cheap adventure. My advice is give it a go, the down side is limited and it might work. And you get massive geek cred if you luck out! :)