Your car uses electronic modules for the engine, transmission, abs, traction control, hvac, instrument cluster and body. They use a 12v power system with 5v reference circuits for the computer boards under low amperage. Its a reliable system. But when you cross the polarity between two batteries like you did, that doubles the voltage to 24v. You were at 24 volts in excess of 100 amps of current which can be seen by your blown 100 amp fuse. But that fuse was made to blow from 100 amps at 12 volts. The higher the voltage, the lower an amperage to do the same job. Thats why things like your water heater in your house and your clothes dryer use 220 volts instead of 110. Thats why a 110 volt extension cord, with 3 wires in it, is so small yet can power so much yet your 12 volt car has each battery cable as thick as an extension cord. Think of voltage as pressure, and amps like gallons per minute. Typical 12v is like a garden hose, 110v is like a pressure washer. The higher the pressure, the less flow you need. But when that 100 amp fuse blew, it was under DOUBLE the voltage (pressure) so the amperage (flow) was cut in half. So a 100 amp blast at 24v is like a 200 amp blast at 12v and something this was never designed for or protected from. 24 volts in excess of 100 amps is the amount of power capable of welding 1/2 thick steel together. So when it gets to a printed circuit board with micro transistors, capacitors, diodes and such that use circuit lines you have the check with a microscrope, and when they get to relays made to control small amounts of current, its like if you walked over to your dryer outlet and shoved a fork inside it. Is this making sense? We're talking about modules that cost over $1000 apiece just for the part before having to be reflashed by a dealership to even allow the car to start, and even then the wiring harness itself might be so badly damaged along with the thousands of dollars worth of sensors on that car that it could very well be totalled. Thats the doomsday scenario, but I've seen it happen. I've seen mufflers get welded on at 18v with the battery still connected do very serious damage. This is worse.
You might be lucky here and just have fried a relay. Perhaps a battery cable. Maybe the battery is the victim. Pray this is the case. You need to do some testing to find out.
First, make sure your battery is fully charged and has been tested and verified good. Most parts stores will do this for free. Make sure the connections to your battery are cleaned up shiny and corrosion free. Verify that they are tight and you cannot move the cable on the battery.
Using a 12v test light (cheap little thing at any parts store) clip the wire onto your battery ground and place the probe on the small trigger terminal of the starter. Have someone put the ignition switch into the start position. If the test light comes on, you are getting signal from the starter relay to the magnetic switch in the solenoid to engage and it isn't doing so. From there, you would need a digital multimeter to do a voltage drop test which is actually simple and if we get that far I will explain it to you. If it passes voltage drop testing of the power and ground cables, the starter would be confirmed bad and it wouldn't be guessing or wasting money on an expensive part to install the starter.
If the light doesn't come on when the key is in the start position, We will be testing the starter relay and relay circuit integrity.
Need to get the engine to turn over to find out what if any other damage has happened from this.
Please perform these tests and post back with the results so I can guide you further towards a diagnosis.