Here's something that two people I know have struggled with.
Both -- despite my insistence that they adopt Time Machine for backups -- managed to lose the iTunes library to which they had synched their iPads. Upon setting up a new library, their choices seemed to be:
Erase the iPad and start over with the new library.
They both opted for the former choice and had to set everything up all over again.
So the questions are:
Is there a third choice? Namely, use the info on the iPad to restore a lost iTunes library without losing info on the iPad?
How does iCloud factor into this with less dependency on synching to a single device? (the incidents in question occurred pre-iCloud)
I have seen this happen, and in fact, I've chosen the wrong option. I have done the same with "Notes" I kept, and erased them all, never to find them again. Although I don't have a tried, true, or tested answner, I will tell you what I'd try.
I'd connect that iPad to a different PC other than the one I sync with. When prompted to erase all data and resync, I'd say no. I'd stop any processes before they start. Then, I'd open My Computer on a PC or Finder in a Mac, and copy everything on that iPad to a folder on the hard drive. (You are saying the data is still on the iPad, right?) I'd guess then you could install iTunes there, tell it that's the folder to look for media and rebuild your library, and cross your fingers that it finds that media and can rebuild. Perhaps then you could copy that library back to the old PC.....
Is this what you are asking? I understand this problem, but do not have a solution for you. I will assume you've searched the Web.
The cloud is new to me as it is to you. I've played around with it, but haven't had time to learn all there is to learn.
Perhaps other readers can pipe in here - It is a difficult task, I can tell you that.
Fortunately I haven't run into that situation yet with my iPad, but I did once with an old iPod. My idea of just copying files from the iPod to my hard drive really didn't work out for me. Not only were the song files randomly named and randomly distributed among randomly named directories, but the files didn't even seem to break at song boundaries. That is, I had parts of two different songs in the files I tried to play. Weird stuff. I have no idea if that experience was typical, or is still the case today. There are several cheap-ish utilities that claim to be able to back up the songs off your i-device though. If I was desperate, I'd use one of them.