Wow that SliMP3 thing is pretty nice. It's unfortunate that you can't play iTunes Music Store files on it though, I've been getting more and more of my music from there now. The same thing happens with my TiVo and the Home Media Option. Maybe part of Apple's big announcement on Thursday will have something to do with this issue (along with the Windows Music Store)
Anyways, enough with my thing, try opening iTunes and choosing Export Library or Export Song List under the File Menu. Beyond that, I don't know what to do, but I guess it will spew out some files and maybe you can choose import on the other computer? I donno...Good luck with it though.