Okay, making the switch is quite simple.
Log in to your account. Click on "Hosting and Servers" and then "My Hosting Account"
Click on your domain from the list on the left.
In the right hand window, you'll see a link that says "Switch Operating System" - click it.
Then you get a bunch of radio-button options. Find the account that's the same cost as yours, but says the opposite. The choices you should make are one of the following:
Economy Hosting w/ PHP - $3.99/mo.
Deluxe Hosting with CGI - $9.99/mo.
Deluxe Hosting with CGI - b - $6.99/mo.
Premium Hosting w/ PHP / PERL - $19.99/mo.
Premium Hosting w/ PHP / PERL - b - $14.99/mo.
(I guarantee you don't already have one of these selected, so pick the one that's the same price as your current one.)
Click the continue button.
No need to phone them.
No need to try to work around it with the windows hosting (I'm here to tell you, with 9+ years experience with GoDaddy, hosting WP on windows server is NOT going to work without MAJOR amounts of tweaking and editing, and will in some way, wind up borking your site. Just take the 3 minutes to make the switch, wait for it to actually switch (10-15 mins) and be done with it.)
You shouldn't have any problems with your old stuff, but it's a no-brainer: Make a back up before you do this.