David - it sounds like you broke the latch on the flex cable connector for the LCD. The part that is actually attached to the logic board, so it may or may not be an easy fix.
I don't think it's feasible to get a good connection for the LCD without keeping the latch in tact. Can it be done? Probably. Should it be done? Nope. I've been able to find a new latch for the iPad 2 previously, but haven't needed one yet for the iPad 3.
It doesn't look like iFixit carries the part, neither do my normal suppliers. I had to browse through Chinese supplier sites until I found someone who carried it last time. I'd suggest you do the same. I looked around, but didn't see anything right away. If you can't find it, leave me a comment and I'll see if I can dig up a link.