The suggested option did not solve my problem.
I used the iOS: Backup and restore your iOS device with iCloud or iTunesoption as it applied to my situation since all of my music from the old computer was already transferred to Music>iTunes>iTunes Media. My iPod shows playlists, play counts and last played dates that correspond to the old computer and the data that I transferred to Music>iTunes>iTunes Media on the new computer. The iTunes on the new computer show my music in the iCloud with playlist, play counts and last played dates that are from an earlier time as I had problems getting access to the iCloud on my old computer and had not been able to sync my iTunes library with iCloud on the old computer for some time.
I followed the steps in the option listed above and was able to create a backup and restore the backup. However, that did not impact my issue at all.
In summary, my issue is that my iPod and the music I transferred to the new computer to Music>iTunes>iTunes Media have current playlists, play counts and last date played while the new computer in iTunes show songs in the iCloud with playlists, play counts and last dated played from an earlier time period. I cannot get the iPod and the iCloud to sync.
On the old computer when I had access to the iCloud, I could attach my iPod to the computer and sync and the iPod and iCloud would then be in sync.
