IPhone :: Transfer Music From It To A Computer With A Different Music Library?

My brothers computer broke. It was a PC. But he had his iPhone synced with it. So now he wants to get the music he lost in that computer to download to his new computer. But the music he purchased is on his iPhone, and the computer wont let him transfer the music from his iPhone, to his new computer. It tells him this music was synced with a different library and won't let him transfer the music.

Does anyone know a work around for this. I know he is using a PC, but I figure, and Apple user, who brakes his Laptop(I'm not talking about crashing, I am talking about actually braking, it was smashed basically), would run into the same problem, your iPhone has Music that was synced with another Library, and it wont let you move the music to the new library. Even though this music was all purchased with the same Apple ID, that doesn't seem to matter. Now, I know that one of the new features of iTunes lets you re-download music you purchased and may have lost, without having to purchase it again. But none of the music from that broken laptop appears in that list of re-downloadable music. All was purchased from iTunes.