If the drain doesn't drain at all, that's a problem. But if the water is draining between cycles but not at the end, I think I know. Is the water soapy, or is it just the rinse water? There's probably a removable strainer at the bottom you can remove and clean. Check for debris, and also whether it's sticky. Sometimes people wash their recyclables, and the glue from the labels collects down below. Clean in hot water with dishwashing liquid to dissolve grease.
The other thing is, there is a gasket (a rubber strip) keeping water from going up inside the door. If the water works its way up inside, then it's going to drain out at the end of the cycle and collect in the bottom after the regular drainage part of the cycle is over. If that's true, you may find some black rubbery residue in the drain. Also, run your finger along the bottom of the dishwasher at the edge where the door collects - see what you find.
If that's the cause, it's just a gasket (cheap replacement by an appliance repair company.
I agree, absolutely do not use Drano. If it were a drain problem you would probably see it in your kitchen sink as well.
To get rid of the standing water, try advancing the dial to the end of the rinse cycle just before it goes into the dry cycle. Close the door and push the start button. Listen for water draining below your sink drain. If the water sound stops before the dial advances to the "dry" cycle, great. If not, or if you're not sure, turn the dishwasher off and repeat the last step - the idea is to get all the water out of the dishwasher. If you then advance the dial to the end of the dry cycle, just before "off", you may hear this sound again. If it's draining, great. If it's not, that's a valuable piece of info to give to your repair person.
Hope this helps.