Thank you, Judysings for your help. Unfortunately, I don't have a backup; if I did, it would be in storage with my main computer (along with nearly everything else I own). I found elsewhere that several people had asked the same question, so I'm not alone in this. I did find an answer in another part of this thread, though. It seems Apple will only let you use 1 computer at a time, even though I authorized this computer with my Apple account; therefore Apple doesn't let you do what I need to do. Apple will only let you transfer music you've downloaded from them. I don't download music; I want to own the original CD of all music I like for playing on my main good stereo system (compressed music in iTunes sounds like crap played through a good stereo, but it's fine for headphones through an iPhone or iPad). I have over 1000 CDs that I transferred to iTunes. Apple's only other way is through computer sharing. This is awful because my main computer has been in storage for months, along with all my other belongings. If it had died or needed the hard drive wiped and re-loaded, I would be screwed as well. Another kind user told me of a third party software called TouchCopy. I downloaded TouchCopy 12 from Wide Angle software, but it would only let me transfer 100 songs with the trial version. I wound up buying the full version for $30 and it was worth it to me. It transferred everything. I had to go through it several times and look for the red X next to the songs that didn't transfer, and re-do them. It took about an hour to do approx. 15 GB of music. All my CDs were legitimately purchased, I don't illegally download or share music, this is for my own use on my own computer and iPhone, and still Apple screws me. All in all, the restrictive way Apple handles (or rather blocks you from handling) my situation has me considering switching to an Adroid based system when I replace my phone.
