They typically don't have anything fancy, just a universal motor. There is a minuscule chance there could be a circuit board, but I would be surprised to see one.
If your inverter not providing full voltage was the problem you should have felt, and smelled the problem, as the windings got hot.
As was said, it is most probably the switch, or the brushes.
The brush holders are typically on the outside and pretty easy to get to. Depending on how much respect you have for electricity you can check the switch by pulling the brush covers, withdrawing the brushes, turning on the plugged in sander, and checking the voltage between the brush leads. If the switch is good there will be 120-volts potential across the leads. Just be careful, because if there is 120-volts, it is enough to do serious harm.
If you don't have 120-volts showing at the brush leads the switch is most probably the culprit.