Plumbing – better way to join two corrugated pipes

I would just remove the garborator if it is unused. Over time, it will become clogged since it's internal holes are smaller than that of a normal drain. You could try cleaning it out by throwing some lemons in it and running it for a while.

Your real problem may be a clogged drain though. In the good drain, fill the sink completely and let it drain. If it becomes slow at any point, you need to have the drain cleaned.

You have a clog somewhere in your line. The first thing to do is check out your P-Trap because it's fairly easy and doesn't require any tools (assuming the nuts weren't tightened by Hercules). If that doesn't work then it's time for a snake. Snake by removing the trap and going in under the sink. Then you won't have to navigate the P-Trap and will have an easier time.

Look around for cleanouts. If you can't reach the clog from under the sink, moving to a different, downstream access point might bring you close enough to get it.