05 Wont Crank after sitting 6 weeks

I have searched for almost 2 hours and cant find any answers so I am hoping someone can help. I will try to keep this as short and sweet as possible. I have an 05 automatic with 86k miles. I put in a new, upgraded starter at the end of September. I drove my car last on October 31, for several hours, off and on (50-60 miles total), came home with the gas gauge on empty and parked it. It got super cold and icy, so the car sat for about 4 weeks. We tried to start it with no luck. I added 2 gallons of gas, hooked it up to another car with some jumper cables, tried a few more times, ended up getting it to start, it had a very rough idle and died (I think it was flooded). The car sat 2 more weeks. I put a few more gallons of gas in it, charged the battery, then hooked up the battery to some jumper cables for some extra amps, and tried to start it, but it wouldn't crank, it just makes a funny whining noise. We held the gas pedal down and cranked several times, but there is no difference in sound or the way the car is acting. It refuses to crank, it doesn't even try. The belts are turning, but it sounds like the starter isn't engaging, it is just freely spinning. I know the starter worked fine, because the car started fine before it was parked. This is my first rotary, and I don't know a ton about them. Any suggestions?



ETA: I just got the car in July, and don't know the history on what has or has not been done, other than the starter, a new radiator, and a new coolant reservoir. I do have hot start issues that were not resolved with the new starter (hoping and praying for them to be fuel pump issues, rather than compression issues). I am wanting to do a compression test, but can't do that until I can get this stupid car running!