I have pulled and pulled... no cigar! There is no other access. HELP!

Can you remove the back panel and push or tap it loose?

LOL, I waited all summer to get one drawer full of tee shirts out of a stuck drawer (I didn't care enough to do anything about it though). Try a hair dryer. If no cigar still, leave a lamp with a bare bulb (not CFL) as near to it as you can all day and night.

Yes, a hair dryer would help. Can you get on either side or bottom? Perhaps a small fan would help too but heat and drying would be a better suggestion.