My top-loading Whirlpool washer stops midcycle...the same exact spot with every wash. We have to slam the lid closed a few times to get it to start up again. Any idea how to fix?

bad lid switch,open the lid a few inches and close it down,if you do this a few times and don't hear a clicking sound the switch is bad.
http://www.youtube.com/watch?v=PZAbg9uftos

Would suspect you have a bad lid switch, may instead have a problem with the neutral drain of the transmission, but suspect you only need to replace the lid switch. The control panel is secured at the end caps, usually screw in back, or putty knife in base to release, control panel rotates up, remove whole cabinet if necessary, all front serviceable,(if it stops in the same spot it is in the timer though)
hope this helps

more than likely lid switch has failed or lid striker is broken use a pen and activate the lid switch if you hear no clicking sound the switch has failed.let me know how you went

This is likely to be a problem with the lid switch.the lid switch is activated by the lid stricker when you lower the lid.these machines will normally fill & wash without needing the lid closed but when it gets to spinning & draining the lid must be closed,so the machine is acting as though the lid is open.the lid has probably been dropped or slammed shut & this can break the lid switch from where it mounts with 2 phillips head screws.

your door switch is going bad,
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lid switch

on the inside of the lid there is a lid switch hole that a plastic tab goes down through the switch could be bad or the screws holding the switch in could be lose or broken

Check your water level switch for a blockage in the air hose.
Check the kid switch for good contact.

sounds like a lid assy issue, can you hear a "clicking" just before the lid is closed, try opening nad closing a few times listening for a distinct "click" if not the machine doesnt think the door is closed and for safety reasons wont spin and drain.

If the problem lies with the contacts, then the knob is not the direct problem, it would be the selector switch behind the knob. Although I don't understand how leaning on the to makes the machine work. Are you sure it is not the switch that indicates when the lid is closed? Either way, Yes!! you can simply just change the switch over.