Crossing the jumper cables doubles the Voltage on the system: 2 x 12 Volts = 24 Volts! Voltage is pressure to push electrons through the electronics. It can fry a lot of components, in a short amount of time... It is possible the maker put in a protective circuit, to prevent over-voltage damage from reversed cables. It costs them money to do that, so they may not have done it.
If the fuses do not fix it, you are likely looking at replacing circuit boards. I was an Electronic Technician for 3.5 years, doing component level repairs -- replacing resistors, diodes, transistors, capacitors, etc. I worked on Switching Power Supplies for computers: high wattage, high voltage, with literally explosive failures. It was always fun to turn on a repaired Power Supply for the first time, to see what happened... I wish you the best of luck. Cheers!
