I would test the motor first, that is the most likely point of failure. I worked on swimming pools and to a lesser extent hot tubs one summer and typically the motor will fail from worn out brushes, much like a starter or alternator.
The motor will try to start, and I can spin the impeller by hand
When it wants to kick in, I can spin the impeller and "jump start" it
If I do that, it keeps running untill it reaches the right temperature, and shuts off
So, the plan is to take the wet end apart and clean it
Like you said, look for scale build up
If that doesn't help, it is probably the starter on the motor