A few weeks ago we had the same problem with our Hotpoint washer. We did a search on the internet and looked for possible solutions. The pump started to humm when it was supposed to drain, so we knew the control board wasn't the problem. After disconnecting and cleaning the drain hoses the pump worked one time, but then quit again. It made a squeeking noise and got really hot, so we stopped messing with it. We got a replacement pump from an appliance store for $35 and it wasn't hard to switch out. We were told that it isn't that uncommon for a pump to break after three to five years.

We used an aquarium water siphon to get most of the water out of the drum. Then we disconnected the drain hose, but be sure you have some kind of tub or bucket close by that is big enough!
If you don't have a siphon, you can try to scoop the water out using large cup or something like that. Good luck!

could be the water solenoid on the drain side

Thanks for both of these tips. Will have to google "water solenoid" tho.

Possibly the safety lid switch is the problem. The switch typically (on older machines) does not come into play during fill and agitate phases of the cycle. What the machine does at the start of the "rinse" phase of the cycle is drain the wash water, then a short spin. The actual rinse sequence is a fill and brief agitate (typically indicated as a dot or asterisk on the timer). There is no "water solenoid on the drain side" on these machines. The motor is reversible. It runs one direction for agitate, reverses direction for drain/spin. Assuming the machine in question isn't a very early specimen of the direct drive design, it does a neutral drain by way of some cams presetting in the transmission during agitation. The motor pauses for a few seconds after agitation (wash or rinse), then reverses direction which shifts the mechanism into neutral drain (no agitate or spin). After a timed drain (typically 2 minutes), the motor pauses again for a few seconds to allow the transmission to "drop" from neutral into spin mode, and restarts in the reverse direction so spin can proceed. Drain itself is controlled by which direction the motor runs. In the agitation direction, the pump forces the water back into the tub. In the reverse direction, it pulls the water out of the tub and to the drain. The machine will always drain whenever the motor runs in the reverse direction (unless the pump is clogged). The lid switch is tied into the "reverse" wiring of the motor to prevent the machine from running in spin (or drain) with the lid open ... thus if the lid switch is bad or not actuating, the machine will agitate but not drain/spin.

Either the actuator on the edge of the lid which pushes down the switch when the lid is closed has broken, or the switch itself is bad. Visually observe if the actuator is intact. If so, press the switch down with your finger or suitable object. The switch should make a faint click when pressed. If it does not, or it does but the machine still doesn't drain/spin, then the switch itself is probably bad. Or the motor is bad for running in the reverse direction. Or the timer is bad for sending current to the motor to run in the reverse direction. But I'm betting the lid switch, it's a fairly common occurrence, is not an expensive fix, and is a DIY job for a competent handyman.

Thank you so much, Dadoes. Needless to say, I knew none of this. Had to read it three times to understand it. But I checked what I'm assuming is the actuator switch, from your description. It is intact. I saw the little slot it's supposed to go into. I stuck a ball point pen in there and the machine immediately did what it was supposed to and spun out all the remaining water.

So that seems to be the problem area. I'm not sure how to fix it but a repairman is coming tomorrow. It's great to have zeroed in on the problem. Thank you very much.

End of story for anyone who has a similar problem:

The repairman came and said it was indeed the safety lid switch that had gone bad, as Dadoes suggested. The part was $30 and labor $55. It was a fairly quick job and I am back to doing laundry. Thanks again.

If you were my neighbor, I'd have done the job for you for free, but of course you'd have to pay for the part. :-)

in my case it was my: "LID must be CLOSED" switch that was defective - I simply eliminated the SWITCH & twisted the two wires together + crimped on a wire connector & water-proofed the connection with some LIQUID-ELECTRIC-TAPE --- now I must remind myself NOT to reach into a Spinning Washing-Machine ... ie: the 10% TEST