There are some copper bands the run from the main board to the screen that have small black blocks soldered in the middle. Heat from the tv can cause the blocks to have bad connections. As of the last time I checked there is no quick or guaranteed fix. I however took two of mine apart and bought a pack of the smallest black paper clamps and clamped the blocks to the strips and then removed the crome wire finger tabs from the clamps because they will be in the way and mine work fine. There's a couple you tube videos that show what the problem is and how to locate the problem. This fix is my idea sorry no video of the fix that I know of.
Some machines must be level and the load in the machine must be balanced. When you unplug and plug back up you are resetting the safety controls on the machine. As your saying it does this every time I would make sure the machine is level.
There are safety switches on the bottom of the seat, at the gear shifter, on the blade engage lever, and on the bottom of the mower at the clutch pedal arm. Most likely the jarring most likely either unseated on of those switches or the wire connector at one of the switches jarred loose.
You can interchange the power supplies but there's a few things you'll need to check first. The output voltage cannot be more than three volts higher than the original, the polarity on the device side must be the same, and the plug on the device must be the same size.