Something you could try first would be to find one file then iTunes should ask if you want it to find others. This may take some time and will only work if you have iTunes' preferences set for it to manage and organize media.
Otherwise you need to consolidate your files to the new media location (make sure you have room because iTunes will copy them to your destination).
iTunes 12 for Mac: Change where your iTunes files are stored - http://support.apple.com/kb/PH19507 - This should say "Change where your media files but not where your other library items are stored" - more information at: https://discussions.apple.com/message/22026652#22026652 - and steps 5-8 in https://discussions.apple.com/message/24491967#24491967
May 2016 post by Kenichi Watanabe summarizing consolidate process - https://discussions.apple.com/message/30216507#30216507
Thanks Limnos. I tried your first suggestion to find one lost file. iTunes did not do what it 'should' have; i.e. it did not ask me if I wanted it to find others. (that would have been great!)
You then suggested consolidating files to new media location. Not sure why you say 'make sure you have room because iTunes will copy them to your destination' ... as I mentioned, I had already manually copied to the new location. So I don't want it to copy them there again.
I looked through the other posts, and tried a suggestion there: File > Library > Organise Library.. > Consolidate Files. This didn't work, still files that iTunes couldn't find.
I then tried something which wasn't mentioned in the posts, since I saw it in the menu: File > Library > Consolidate Files. That created duplicate entries in iTunes, one that plays, and the other with the ! symbol to the left. (I tried to insert a screenshot for you in this post, but when I pressed Upload, nothing happened).
iTunes doesn't allow me to sort by that column on the left; if it did I could select all of them easily and delete the extraneous entries, and I don't wish to do it one by one (13,000+ songs).