I am also having the same problem with a refurb fone i recieved yesterday, and i need my keyboard badly, nonetheless reading everbodies post i decided to use a guitar pick to wedge the keyboard out of the case housing.
I inserted the guitar pick in the middle underneath the space bar button and wedged in, and proceeded to wedge from left to right and back to middle until the keyboard became loose enough to slightly begin to peal off, starting from back to front BUT i did not remove the keyboard completely (because i got scared lol) and decided to put it back how it was and run my fingers firmly and repeatdly up and down to reseat the keyboard back in place.
This helped alot, it isnt perfect but it gives me enough functionality to wait for my other refurb phone
.....hope this helps and if your scared you might break the keyboard and or dont have a guitar pick, I DO NOT RECOMMEND YOU DO IT. A guitar pick is plastic and does not damage a keyboard like a small metal screw driver would.
Thanks for all your posts and I hope everyone here gets a new mogul