Can't re-download Mountain Lion (recent purchase)

Question

I recently bought Mountain Lion from the online Apple Store, went through the rigamarole with the encrypted PDF, and downloaded it. In the App Store, it is now listed among my purchased software, but when I attempt to download it again, I cannot. Earlier today, when I tried to re-download it, App Store asked me to log in with a different ID. It was NOT the ID I had used in the online store to purchase ML, so that made no sense to me, but I tried it anyway. When I logged in with the different ID (which I have used so seldom, I didn't even remember that I had it), it didn't show ML as a purchased app, not surprisingly. When I went back to trying to use my main ID, I just got the same old crap telling me to use a different ID.
Tonight I get "We could not complete your request. There was an error in the App Store. Please try again later (100)."
What is the problem? This does not inspire much confidence in Apple's online services.

Answer 1

When I tried to invoke Time Machine it said no useable B/U could be found, even though I'd been using it all along and was surprised there wasn't one. I don't have any other B/U system except my old internal HD with everthing on it--including ML OS. 
I'm not going to risk quitting the installer to try to save the huge ML file I'm still downloading; I'm going to just go for the automatic installation. I'd have to DL it again anyway even if I knew how to save a copy of it.  My understanding is it goes away once it's used--which is why I couldn't find it on my old internal disk. 
Update: as of a few minutes ago, after about the fourth attempt, I was able to update SL to allow me access to the Apple Store.  I did this by first making a new administrator account in SL that did not require ANY password. I reasoned that I would thus be able to gain entry no matter what; apparently it worked, or something else did this trip around the merry-go-round. 
Right now, I'm  stilll downloading the Mountain Lion update (glacier speed, of course). 
The final test will be if the whole thing blows up when I install ML.  If it does, I'm wiping the HD and starting completely over.  I'll then try to move my files folder by folder onto the new HD and go through the ordeal of reinstalling all my software again.
This is a true PAIN in the butt and time waster.  One would think that the updaters would be able to recognize and simply delete or quarantine incongruent system files so they can't wreck things.  And one would think there was a non-magical/secret way to download and make bootable a copy of any OS. 
Thanks for your reply.