Your machine has what is caused a neutral drain. When the machine drains, the transmission is in neutral, so that it is not trying to spin with a full load of water.

Once the timer has operated the drain long enough so that it thinks the water is drained out, the timer will stop the motor for a few seconds. This will cause the transmission to shift into spin mode. In your situation the timer is not doing this pause, so the machine never goes into spin mode. When you open the lid or push in the timer to stop things, this creates the pause that causes the transmission to shift into spin so that you can now get the spin cycle.

You will probably need to replace the timer, but before you do that I would spin it fast a fair number of times. Sometimes this will loosen up things so that the timer will now go into pause. If this does not fix things try replacing the timer, this part here. Of if you don't want to spend that kind of money on this machine, just remember to raise the lid. It might even fix itself after some weeks or months.

Part number: AP3019073