I don't have a Mac available to me (the logic board died). I have my whole Mac backed up on an external HD by way of Time Machine. I would like to copy just the music to my new Windows 7 laptop. I don't mind if I have to install iTunes. I have heard of a program called "TransMac". Will that work? Or is there another program/method of accessing the files?
I'm pretty sure Time Machine disks always use the Mac HFS+ format, so you'll need a way for Windows 7 to read a disk in the Mac HFS+ format. Apple ships a read-only HFS+ driver for Windows as part of Boot Camp, so you might be able to get ahold of that driver and install it on Windows 7 and read your Time Machine disk.
It looks like TransMac won't do it. TransMac apparently lets you open disk image files, not whole hard drives.
If you want full read/write access to HFS+ from Windows, you can get Paragon's HFS+ for Windows for US$20.
Once you have a way for Windows to mount your HFS+ disk, you'll be able to navigate to the folder with the Time Machine backups, find the one with the most recent date, find your iTunes library in there, and drag it over to your other hard drive.