Sorry I do not recall exactly who had ths same problem, but it came in handy with my reading here. We had what we thought was a busted garbage disposal. Since that same side also is where the dishwasher drains, we were about to get a new one.
Silly us. The only reason is sounded funny and wasnt draining, was the pipe on the other side was clogged. Someone with a double sink like ours had the same problem and was also just like us, thinking if the one sink drained, it had to be the disposal. Someone here called him a nitwit (gently) and pointed out the easy thing to check first if PVC pipe is the other side of the disposal. Yup.
Grin, I'm sure I'm not the only one here who's been about to do something dumb then remembered a post and found a simpler answer!