I put some freshly cooked chicken strips(that didn't smell right) down the disposal and it clogged up. Thinking it was just a mass glob of bad chicken blocking the drainage, I unscrewed the hole under the pipes to snake the pipes, and of course got a big blob of ground chicken. Now I can't get the water to drain past the disposal. The disposal seems to be working. It sounds normal, and the bottom spins as it should. Any ideas what is wrong and how I can fix it without calling an expensive plumber in?

I unscrewed the hole under the pipes to snake the pipes,
Would this "hole" be a clean out plug at the bottom of the bend in the trap? This is to drain the trap of built up sediment not to run a snake up into it. To snake the line the "J" bend of the trap must be removed. This might clear the clog but if it don't send a snake sent up into the wall for about 8 feet. You will hitva elbo about 7 inches in but once around that you're home free.
Good luck, Tom