Hi KimLaF,
Which Store are you looking at? If you are looking at the "Purchased" option under "Store" in the sidebar, that is the problem. You need to click on the iTunes Store itself, and open the Store. Once it is open, go to Quick Links on the right and click on Purchased. Then you will see tabs across the top where you can view Purchased Music, Movies, TV Shows, Apps, etc.
Click on Not on this Computer. You will see a list of all the items which have been purchased but not downloaded to the computer with a little Cloud with an arrow in the center next to each one. You can click on them selectively, or click on "Download All" at the bottom.
Be sure the computer is Authorized - Click on the "Store" option in the menu at the top (I know - how many various places does the word Store show up? - I think this is the last place where it is and where it means something special....). Once you click on that Store, you will see an option to Authorize this Computer. Click on that if you have not previously authorized.
Cheers,
GB