If you don't think you can fix the airport cable yourself -- it should be a matter of just splicing one or two wires together, then what I would do is buy a cheap USB wireless adapter which can probably be had for under $30 for 802.11b/g and under $50 for 802.11n.
Thanks for the feedback and advice jw2002. The splicing sounds easy enough - have you seen any tutorials w/ pictures on this?
The wireless adapter sounds good too, but seems a little on the messy/cluttered side of the solution. How would I make the Mac Mini not use the airport but rather this?
That's the same store I goto for my Apple stuff (and also Annapolis Mall if I'm in the area), pretty good store.
I personally don't use the bluetooth on my mini (at least I haven't yet) so that wouldn't be a huge deal with me but I would also recommend just running a CAT5 cable to your router since it's so close and your mini is going to be stationary.
yeah, that's what I'll probably go with too - at least temporarily, but it'd be nice to have the wireless working for random situations (taking Mini somewhere, another room temporarily, etc)