I read your post 4 times and have no idea the story behind you trying to transfer your music. However if you want to transfer music between two computers, (not cpu) there are various methods.
1. One would be using a flashdrive, by plugging it in a usb drive, and drag and drop the music onto it, remove it, then drag and drop it onto your other computer. Flash drives can be very inexpensive. If you don't know what a flashdrive is.
USB flash drive - Wikipedia, the free encyclopedia
2. You can also burn it onto a Cd.
3. You can archive all your music into a .rar or .zip file. Send it over aim or other instant messaging program.