Here are your parts
Replacement parts for HDA3700GWW models | AppliancePartsPros.com

[COLOR="DarkRed"]Is it possible that there is a problem with the dial? [/COLOR]
I doubt it as it sounds like the wash/drain solenoid is pulling down.
Remove the kick plate and take a look to confirm this.
The way the drain works is that the timer activates the wash./drain solenoid for a couple seconds. This pulls the solenoid down, switching the flapper valve to the drain position. The water pressure then holds the flapper in the drain position till the unit is empty.
Sounds like you are not getting enough pressure.
Usually if it is a timer problem, it activates the solenoid for too long which causes the solenoid to overheat and melt the plastic in it.

[COLOR="DarkRed"]I was thinking that maybe it was an issue with whatever motor runs the draining . . . but why would it work sometimes and othertimes not? [/COLOR]
There is only one motor in the unit dor wash and drain.
If it is washing OK then your motor is OK.
A common problem with these units is a bad Piston & Nut (Item 564 in Section 2). It is under the screen filter at the back of the tub. It unscrews.
What happens is that if it does not seal correctly water is directed back into the tub instead of out the drain.
I would start here.

Since you are working on it, I would also remove the sump cover (middle of tub floor) and check/clean out the sump. Take note of how the internal piece is installed. Re-install it wrong and the chopper will eat it. Also check for twist ties etc. wrapped around the chopper.
Be careful as there is often broken glass in the sump.

If you empty the sump to see better be sure to add a couple quarts of hot water to the unit before running it. These pumps will burn up the seals if run when dry.