2011 RX8 won't start! Please Help!

I have a dilemma, I went out of town for 3 weeks and when I got back my car wouldn't start. I called a tow company to come and jump the battery which didn't solve the problem. The car would rev but not turn over. I made an appointment to have it brought to the dealership to have it looked at. Before being towed to the dealership the company tried to jump it again and it did nothing but click this time when the key was turned. Mazda says it could be two things; the keyless entry got ruined during the jumping process (they think the battery terminals got put on backwards at some point) or the ECU got fried. They can't tell for certain and want to replace both, one at a time but no guarantees. I don't really trust them or have faith that they know much about this car. I've been reading posts on this forum all weekend about similar situations and everything seems to be applicable to what I'm going through. Can anyone help with some tests that could be done that would eliminate the ECU being fried as a possibility? As far as Mazda is saying all the power components inside the car work minus the keyless entry. I feel that these things they came up with are only part of the problem, if jumping the car caused more problems what was the initial problem to begin with?!? Ugh please help! 😩

2011 RX8 won't start! Please Help!