We are running our dishwasher (well now it's off) and we noticed water running out from the bottom of it. It is clear that it is not draining. Looking in the main sink, and the prep sink, and both are filling up halfway. The prep sink is filled with lots of food and waste. Both sinks have insinkerator garbage disposals, and we never put heavy duty food in them. Thinks like left over rice, pasta, etc, and always with them running with water. Anyway, since both sinks are overflowing, I assume its the return pipe that both must be connected to.

Can I put a snake down, even though I have garbage disposals? Can I just load up with Liquid Plumber to try to knock down whatever is causing this?