Sounds like you have some kind of clog that's causing the excess water to pool into your kitchen sink. The piping is supposed to support the drainage of the dish washer. Obviously something is blocking it. You can try turning off the water to your home (a no brainer but it needs to be said sometimes) and remove the plumbing immediately under the sink to see if something is there... Otherwise you'll need to opt for a camera to view what the problem may be.

Retroloco-LJ
FH Furr - Home of the "Plumber in your home for Free"