The 7500 will not spin at all if it thinks the door is unlocked. And yes, they have solenoids not wax motors for things like water valves and door locks.
It could be the belt. And the belt is relatively easy to access and replace. Not too expensive, either. It might be a good idea for a washer of its age just to replace the belt if it shows any sign of wear or slippage.
However, I remember replacing the belt on my 7500 when it was still under warranty. It was making a strange kind of squeak crunch noise with a heavy load. Finally I got the repair service out and he quickly diagnosed a cracked support spider. It took another week to get the part in and have the repair completed. But he said not to use it in the mean time because if the spider failed completely it would have caused a lot of damage.
The machine has been running perfectly since then (oh, there were other warranty repairs around the same time, like motor, motor controller, main board... but that was not uncommon for early 7500's). Now the darn thing refuses to die so I can't justify getting a nice new Electrolux or Miele to take its place, lol.