Thanks for the suggestions; I had already done all that before, but I was able to solve the problem in a roundabout way. First I realized that when I transferred my library to my new laptop using iTunes instructions, two-thirds of the songs came over in icloud status. So I downloaded all those songs and then my library went from 288 to 770, an improvement, but not close to the 1588 I had before transferring the library. So I resorted to going back to my old laptop, downloaded the new songs I'd purchased on my new laptop from the cloud and syncing my iPod on the old laptop.
Now my iPod has 1606 songs, as it should, but iTunes on my new laptop still only has 770 songs. So, if you have any suggestions on how I can make my new laptop match my old one so I don't have to keep it available for iTunes, I would appreciate hearing back from you or anyone who can help. I have never understood how Apple can make such great devices, but has always come up short with iTunes! Thanks.