I did the iPhone Explorer trick and it worked but this is what I did. I have an iPad and an Iphone. Both with latest iOS 4.2. Angry Birds HD on the iPad had the black screen problem. I tried doing the iPhone Explorer trick but after re-installing and restoring DataStore and highscores.lua file the black screen came back.
I connected my iPhone to iPhone Explorer backed up the following: highscores.lua, DataStore, PostManager, and settings.lua
I re-installed AngryBirds HD on my iPad and before opening the App I hooked it up and used iPhone Explorer. There were no files in the "documents" folder. I copied the backed up files from the iPhone (highscores.lua, DataStore, PostManager, and settings.lua) to the documents directory on the iPad. And it worked. I got all the levels that were on my iPhone on the iPad.
I tried all of the listed soloutions and none worked. But when I reconfirmed my credit card info for my appleid when I updated, angry birds worked perffffectly fine.