Why I can't download apps on my iPod through my computer?

I keep trying to sync 2 apps on my ipod through itunes on my computer. I click sync and i have to wait for the whole process of syncing. Then, when I check my ipod, the apps I wanted aren't there. I go to the app store on my ipod and see if I can download the apps from there, but it says "Installed." So, I try to delete the apps on the computer and see if i can download it from the app store on the ipod instead. I sync and wait again, the apps aren't there, I go to the app store and try to download the apps I wanted. But then, I can't press the install button. It's a light blue instead of its usual darker blue color.