I've got a solution, maybe not the best, but it'll work... if you don't have a mac.
You computer might be recognizing your phone as a mass storage device. If that is the case, you're music could be one of a few spots. First I'd recommend going to marketplace and installing 'Astro'. This is going to allow you to see most the phone's files. There is a music file, check that out first.
If that doesn't work and you've perused the deep corners of your Bad-A machine, I'd recommend downloading 'Motorola Media Link'. This is where you'll need a pc bc MAC's aren't supported. I have both and only my vaio ran the software.
After installing moto media link, follow the instructions for connecting your phone and don't forget to mount. If you're not sure what mounting is, a 'USB connected' message will appear under your notifications, click it, push mount and BAM!, you're in. Transfer your music files again, but i'd recommend spending some time searching for that lost music... especially if you've crammed your phone with 10 gigs of tunes.
Moto Media Link is user friendly, but will only allow access to a modicum of the files in your droid...only media... hence moto MEDIA link. Good Luck Bud!
Thats weird that your music isn't in your music app already?? What if your songs didn't really transfer over to the Droid? And you just think they did.....after looking in Astro after you download it, and you still can't find them, then I would say this is what has happened...