iPad won't show apps that used to work

iPad was working fine with many apps. Then I tried to download a large number of updates and it got hung up. Many apps stopped working and could not be deleted. I did a sync, which did not resolve the problem. Then I did several more synchs and updated the iOS, which did work for most apps - but not all!

I have reset the iPad, updated, and restored the iOS, but still there are apps that iTunes shows as installed on the iPad but that are not actually on the iPad.

I tried looking for them in the list of apps running in the background - they aren't there either, and the icons for them are nowhere to be found. iTunes says these apps were loaded, but they are not to found anywhere on the iPad.

Two of the missing apps are Zombie Cafe and Pandora Radio.

I tried deleting them from the synch using iTunes, and then reinstalling them on a second synch. No joy.

Then I tried reinstalling them direct from the store - but it won't let me re-download them. The buttons say the app is free, but the 'buy' buttons are dimmed and don't react when I try to download them.

By the way, these apps are working perfectly on my iPhone 4...

I am at my wits end! Help?