Unable to Sync iPod via iTunes

Hello, my old PC just died so I bought a new one. I have iTunes, an iTunes account, and an apple account. Once I got iTunes set up on my new computer, I found that I could not sync anything to my iPod classic anymore. I added my new computer to the authorizations, but I noticed that my new computer was NOT added to the "Downloads and Purchases" section of my account settings. There appears to be no way to add my new computer to this section. My old computer was in there, and everything worked fine with my old computer. Is there a way to add and authorize my new computer to the "Downloads and Purchases" section of my account so I can sync my iPod again?