Tab-4444 works best if you haven't run through the tutorial and dialed-in, otherwise the software has been upgraded in an attempt to disable access.
If I had another IO that wasn't being used but worked, is there any way to either get the working modem is the old IO, or somehow transfer her account settings to the working IO?
The easy way:
Using the tutorials here on the board, open the functional IO and remove the philips screws from the standoffs holding the modem, then put that IO back together.
Repeat the process for the IO with the non-functional modem, replacing the burned out modem with the modem you removed from the functional IO.
The hard way:
If you really want to swap the settings, you'll have to go read up on the hard drive method, dolly, and other misc topics. It's entirely possible to do it this way, I myself have transferred my settings to various IO's, but it's infinitely more involved than a simple modem swap-out.
It's been covered quite a few times now, so if you do a search, you'll find any number of walkthroughs on the whole process.
Either way, you'll have to open both of them up, so why not use the easier method?