Old iPod needs repair shop--any recommendations?

The setup:

I’ve got a sick 1st generation iPod. I think I know what’s wrong with it,* but the local Apple Store says they no longer repair models that old.

(It’s always a bad sign when the guy at the repair shop “hey, check this out…when’s the last time you saw one of these?” to a passing co-worker.)

I have found a few places online that repair old iPods for a reasonable price, but since I’ve never used one before, I was wondering if anyone could recommend one from personal experience. (I don’t want to mail it to a place that takes months to respond to an e-mail, screws up repairs, or steals and uses customers’ equipment to operate Syrian nuclear facilities)

Can anyone help me out with this one?
*A busted Firewire port, and/or a dead battery. Everything else seems to still be OK.

I’m not sure how difficult or easy it is to change the battery on a first-gen. You can get a battery along with the tools to change it for some models, but I don’t know if it includes that one.

Usually it’s cheaper to replace something like that than repair it, especially since they’ve become cheaper and bigger over time. You could probably replace the battery, or maybe the hard drive if it failed, but anything beyond that would be unusual for someone fix and probably expensive. (Unless it’s something else that’s simple and obvious, like a broken wire or something maybe. I don’t know, I’m no expert.)

Well, from what I’ve read, I think it’s either the battery, or the Firewire port, or possibly both. Luckily enough, one of the repair sites I’ve found does claim that these are both repairable, and for less than the cost of a new iPod.

But, like I said, I’d want to be reasonable sure I wouldn’t just be getting ripped off, thus my need for advice.