The reason the dishwasher is flooding is because it drains into the disposal.
If you have a wet/dry vac, you can use the nozzle to suck the debris out of the disposal. If not, UNPLUG THE DISPOSAL underneath the sink, cover your hand with dish soap so it doesn't get stuck, reach in and CAREFULLY remove any debris.
More than likely, the disposal breaker has been tripped. This is a small red square button on the bottom that needs to be pushed in. If it still doesn't work, there is a hex drive (looks like a pentagon) on the very bottom of the disposal that needs to be turned to help remove any additional debris. Plumbers usually leave one somewhere under the sink. If there is not one, use a broom or plunger handle to turn the disposal from the TOP. Simply insert the handle, move it to the edge and try to turn the cutters.
If you reach in the disposal with broken glass, please be careful. A hospital bill will be MUCH more than a plumber.