Make sure your computer is physically connected to whatever gives it an Internet connection, install Linux, chances are you'll be able to access the Internet from the Linux install. Stop worrying about problems you don't know for sure exist and just try it!
If you want to check things out before committing to an install then get a live CD, such as Ubuntu
, boot off it, and see if you have an Internet connection.
Don't worry about Firewalls unless you actually have a specific reason to worry about Firewalls.