I have a Whirlpool Ultimate care 2 and it stopped draining water and entering the spin cycle. I initially thought it was the water pump and replaced it. The draining lines seemed clear(no issues with draining water from washer, even the ones connected to the water pump ;) ), but I am running into the same issue. Now I've noticed that when I set the machine to rinse(from empty) it filled with water and that was it. When I turned the knob to another cycle for rinse, the knob would begin make a noise kind of like a timer then eventually stop. Not sure if it is something intrinsically wrong with the knob mechanism or the lid switch. Please help!
The most common reason for this is a bad lid switch. The drain function is part of the spin cycle, which will not start unless the lid switch closes a circuit to indicate that the lid is closed. If you are reasonably handy you can jumper the switch to prove this out. Since you already replaced the pump (which, by the way, would be the second most common cause of your problem) I would assume you are capable of testing/replacing the lid switch.
The "timer" noise you are hearing from the knob is likely normal, you just never heard it before because you never had to pay close enough attention to it before you had problems.