Many missing songs on my new computer after transferring the iTunes library

After transferring my iTunes library to a new computer I realized that many songs did not transfer. But my iPod has the entire library on it! The missing songs do not transfer when I sync the iPod to the new computer.

Both my old and new laptops are Dell and the library transferred using a Dell transfer program.

My iPod touch (7th generation) has the entire library on it, but it will not sync any of the missing files.

My Dell is an Inspiron 15 3520.

Unfortunately, I didn't realize this until after I had sent the old laptop to Dell to be recycled (I had cleaned the old Dell of all data).

I have read that I could use a third party app to help make the transfer of the missing files. Is this true? And do you have any recommendations? Or is there another option?

Please realize that I have a limited skillset when it comes to this problem.