Water not draining
Usual causes are:
1. Something in the drain path blocked. Symptoms: You can hear the drain pump running at the appropriate bits of the cycle, but if you you open the door the instant the pump stops, there is still a pool of dirty water in the bottom. Solution: Follow the path from strainer through drain pump to drain hose, find and eliminate the blockage. Most likely points are the strainer and the inlet to the pump. Hint: You can identify the drain pump by following the drain hose and seeing what it's attached to.
2. Drain pump broken. Symptoms: Usually, you won't hear the pump running at all at the appropriate times; if it does run, it won't sound right. Solution: Take it off and open it up, see if something is blocking the impellor (in which case, fish it out). Spin the impellor with your fingertips; If it won't turn at all, you need to find out why it has siezed (may be fixable) can you feel it turning the motor (a very magnetic, "flippy" sensation). If you can't, the impellor has probably become unstuck from the shaft. You may be able to glue it on, but this fix is unlikely to last very long. Use a multimeter to measure the resistance of the motor windings. If madly different from a few hundred ohms, again a new motor might be necessary. Hint: The pump motor and impellor can usually be bought separately from the pump housing as a much cheaper unbranded part.
3. Back-siphoning from the waste plumbing. Symptoms: You can hear the drain pump running normally at the appropriate times, and if you open the door the instant the pump stops, the machine appears to be empty, but then quietly fills up with dirty water. Solution: There is meant to be an air break (or in some installations and anti-siphon valve)where the machine's drain hose enters the domestic drainage drainage system. Unblock/unjam this. Hint: After fixing this, run the machine empty on the hottest, longest cycle it has; some of that dirty water may not originally have come from the dishwasher.