My old Maytag washer won't spin clothes dry. It fills, agitates, and drains fine, but it won't spin -- at least not with wet clothes in it.

When I totally empty the machine, I can get it to spin. But it makes a banging noise and the basket appears to be off balance.

Some other clues:

• There's a burnt smell coming from the washer when in the spin cycle
  
• I checked the drain line and I don't see any signs of blockage
  
• I checked the lid switch and it works OK
  
• We have a cleaning lady that routinely overfills the machine
  

Any help would be appreciated -- thanks!