Question for Mac people

Do I have any of those here? :)

Okay, so Jerome's dad gave him an iTunes gift card, and he bought an album which he downloaded to his Mac laptop. He tried to move it to the desktop (or, more specifically, the external hard drive) so that we can add it to the main iTunes on the desktop. But every time he tries to play it, it wants his password, and then won't play anyway. It says that he's successfully authorized the computer (he can authorize 5 computers, and is only at 3, which is confusing), but it won't play. The desktop is a PC, but that shouldn't matter, right?

He also can't burn it out to a CDR, which was my solution to fix the problem. He should be able to burn something like 5 copies of the CD before you have to resort to other methods of sharing it (at least you could 2 1/2 years ago). This doesn't seem to be a problem with his CD burner, as he burned a different CD with no problem.

Any ideas/solutions? I really want this album on my iPod. :(

UPDATE: In case anyone reading this is similarly looking for the solution to the second issue, it turned out that all he needed to do was run the lens cleaner (which I guess I had bought for the DVD player a while back) through his computer, and all is good now. No clue WHY it worked for the 1 CD he burned, but not all of the attempts of the other one. But it's solved now.