If you see only the songs you purchased, you are probably accessing those songs from Apple's iTunes Store servers (also called "iCloud"). Purchased songs are made available to you, to download or stream, on any computer (running iTunes) or iOS device (like your iPhone and iPad) that you associate with your Apple ID. So, if you get a new computer, you can run iTunes on it and access your purchased songs immediately by associating that computer with your Apple ID. You don't need to download songs to the computer.
Based on the info you provided, my guess is that your Mac is that "new computer." I don't know if the work you did ("I spent months burning several hundred of my cd's to a hard drive") was before or after getting the Mac. But currently, it sounds like your iTunes library is only able to access your purchased songs. They are being accessed from iCloud, not from your Mac's local drive.
You can check by doing a right-click and Get Info on one of those songs in iTunes. On the Info window, go to the File tab. Find location. Does it give a file path to where the song is stored on the Mac's drive, or does it say iCloud?
Some other points that need clarification...
- On the Mac (since getting it), did your iTunes library have those songs your imported from music CDs? Or was that on your previous PC, and not on the Mac?
- Do you subscribe to (pay for) either iTunes Match or Apple Music? These are two Apple services that provide an iCloud Music Library. Otherwise, you do not have an iCloud Music Library, and only your purchased songs are accessible from iCloud. Your other songs (like the ones imported from CD) are only stored locally, on the drive of the computer used to run iTunes.
- Do you still have access to the previously used PC, with its iTunes library intact?