Q: New music won't download to Ipod

I have a new computer and a new Ipod. While the library downloaded, any new music I purchase will not transfer to the Ipod. I have authorized the computer and the new music shows up in my library, but it will not transfer. I try selecting Sync, but that doesn't work either. The only way new music will transfer is if I use my old computer, which is ready to quit working at any time. So I need help in getting the new computer to transfer my new purchases to the Ipod.