Q: New iPhone 7 is not accepting CORRECT iTunes password. Apple support rep unable to assist.

Essentially...

Just got my iPhone 7 plus, set up went great. iCloud is set up along with iTunes. HOWEVER, I have some old songs from an old iTunes account that were on my old phone. (So songs from two accounts on one phone.) My NEW phone continually pops up telling me to enter my old iTunes account password for the songs associated with it, but when I do it either says "incorrect password" or "cannot log in". And yes, it's the correct password. I even reset it.

Any advice?