Are you sharing this computer with anyone? Check to see if you are in fact signed in by clicking in the App Store menu bar Store > View My Account ("your email for apple ID"). Or if you are not signed in it will simply say Sign In. Or perhaps show someone else's Apple ID?
Next I would go to iTunes and do the same (here it will show you more details if you successfully Sign In) Store > View My Account ("your email for apple ID").
If someone els is using their Apple ID be aware that signing them out and then signing in with yours will mean any old DRM purchased music on this computer (you can tell because its 128kbps) will no longer play or sync. This shouldn't be the case for newer purchases. As for Apps, I believe they will still launch but you will not have the ability re-download and install them. Also, iTunes in the Cloud features only allow you to associate a different Apple ID with a device 90 days from the day it was first "Associated". A device is automatically "Associated" with you Apple ID once you turn on Automatic Downloads or download any Past Purchases onto a computer or device which is also Authorised. You can check to see what date a device was "Associated" under iTunes > Store > View My Account > Manage Devices.
But, if this is a new computer and first time App purchase, your problem should be allot more straight forward. Have you succesfully purchased or downloaded Apps and iTunes content with this Apple ID before? If you can view your account in iTunes, check that all details appear to be normal, try signing out / back in. Also try simply quiting iTunes and App Store then reopen.
If you cannot sign into your account by doing either of these things, then I would definitely contact Apple to make sure something isn't askew on their end.
Good luck Rosie! :]