The solutions presented on the page to which @norm123 refers are not applicable here.
The problem is clearly not linked to basic computer settings (firewalls, etc.) which the solutions address but rather to the Apple ID, since one ID works while the other does not.
I am having an identical or similar problem: I have two Apple IDs, where both work fine through the iOS App Store but one does not work in the iTunes Store through the iTunes application in Mac OS X Mavericks.
When trying to login to the iTunes Store through the iTunes application in Mac OS X Mavericks, I receive the error message "We could not complete your iTunes Store request. The iTunes Store is temporarily unavailable. Please try again later."
However, when trying to login to the iTunes Store with an incorrect password, I receive the error message "Your Apple ID or password was entered incorrectly."
As a result, it appears that my Apple ID is being blocked somehow by the iTunes application.
The problem appears to have started when I activated iTunes Match on the still functioning Apple ID, which appears to have blocked the other Apple ID.
I have restarted iTunes and have deleted iTunes preferences (com.apple.itunes.pref) in my user library and then restarted iTunes and my computer. Nothing works.
Anyone had any luck in finding a solution?
've had the same problem for over a month now on my iMac. I can log in using my iPhone and my work PC running windows 7 and when I set up another user on my iMac. It's since I upgraded to Mavericks. I spent 3 hours on the phone with two different Apple technicians 10 days ago. I formatted the hard drive and migrated my Time Machine backup. If it's a possible Mavericks issue you get 90 days free support. I expect to spend another 3 hours on the phone again this weekend
Still nothing. I might just go back to a Windows PC.