a FIREwire interface is like an external soundcard, with XLR and 1/4" mic inputs that you connect to your computer via firewire.
it lets you record multiple tracks so you can edit/tweak each instrument separately after recording, with programs like protools, etc. they are really really nice...
(i'm not recommending this one in particular-- but it just looks pretty).
i'm quite sure the problem with your machine is not the sound card though, but the connector, from what you describe, clearly that's what it is. it should't be more expensive than opening the thing, soldering a replacement, and closing it again. don't let them scam you!
