Hi Limnos,
Thanks for responding. Just having someone else thinking about this encouraged me to not give up!
I think I figured out what happened (thanks also to Verizon Wireless), and thought I'd reply so that someone else might benefit, too.
When I transferred files (and my library) from my old computer to my new one, the music list transferred, but the actual music files were not on the computer (/user/username/Music/iTunes/iTunesMedia). Before I did this, I didn't think to check this folder to see if the artists/songs were actually on the computer. It seems like I did play music through through the computer, which is why I thought the library was there but perhaps sharing was on? In any case, the music files were nowhere to be found. During the sync with the phone, the list was updated to reflect what was actually on the computer so it looked like the library had been erased.
How I fixed this: I still have my old computer with all the music. I connected (using LAN) an available external hard drive to my old computer. I then manually copied the music files to the hard drive (surprisingly, it didn't take long). Then I used my new computer and connected (wi-fi) to that hard drive and imported the music into iTunes,
After importing, the sync to the phone had all the music.