It looks like you haven't read enough about Linux. Linux is an operating system just like Windows is and you cannot install it "ontop of windows" as you would do with an application such as Office or whatever.
As for your other questions: no, you don't have to save all your files. You just need some free space on your HD so you can create the partitions needed for a Linux install. Then you'll need a bootloader to be able to choose which OS you'll boot, Windows or Linux (no problem, every distro of Linux comes with one). After installling you'll be able to listen to your favourite songs without any problems.
Getting access to the Internet from Linux is quite easy. Remember that Linux was primarily designed for and it grew with the Internet.
About slackware...while you seem to lack some knowledge about Linux I'd advice you to first try a LiveCD such as Knoppix or SuSE. That's a CD containing the whole Linux operating system but it won't install to your HD and, therefore it won't touch it. This way you can make a first impression about Linux and then you can decide if you wanna go further with it.
Anyway, read some more about Linux, read the topics here, at the Newbie section of this forum (a great forum) and also some tutorials. In this forum you'll see that many asked the same question as you did and it may guide you in your choice. Also you might take a look at www.distrowatch.com.
and at www.tuxs.org.
Good luck and we're expecting you back to share us your impressions about Linux. You won't regret it!