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Looks like it's been getting warm, but that might be quite normal. Do you have a multimeter?
Any idea what that black thing with the wire coming out of it is? Looks like it might be some kind of reed switch or thermal sensor?Give it the sniff test - anything smell burnt?
Measure resistance across the motor windings (should be a good few ohms, not open circuit, not short circuit).
Check all the connectors, anything loose? Reseating things is never a bad idea if the plastic hasn't gone brittle.
Can you measure continuity from the plug pins to where the wires join the circuit board? That at least eliminates the plug, fuse and the flex and will help you understand the circuit layout a bit more.
The other thing to check is whether the control switches are closing the circuit - how to do that depends on how the switches work.
Oh and give it a thorough clean - you often notice things when you're cleaning that you don't notice if you're just looking (same with bikes).
Don't know what the electronics look like on those but assume they're fairly simple. Start with a visual check for blown components or bad solders then break out a multimeter and do continuity checks. Probably a good chance it's a dead motor.