How can I "authorize" a computer?
There is an Apple support article that gives a couple solutions here:

http://support.apple.com/kb/TS1389

I've also seen people with this problem solve it by downloading and re-installing iTunes manually from here:

http://www.apple.com/itunes/download/

I would try the 3 suggestions in the Apple article first (because they are easier) and then try the download and install.