My Crossfire was given to me by my father. He lives in Texas and I live in Iowa. The car arrived in December and it was kept outdoors with a cover. The cover froze to the ground and I was not able to keep the battery charged. I did not know the basic of keeping the battery charged will it is being stored.

Once spring arrived I charge the car battery, replaced the battery in the Fobs and the car started with no issues. Luckly enough I was successful took the car for a short ride (about 6 mile round trip) to top off the fuel tank. Once I got back home and park the car and 20 minutes later I attempted to start (run) the car and move it into the driveway and it would not start.
So, I thought the key lost synch with ignition and I resynch the key and it started (ran) with no issues. The car sat for 2 weeks and I discovered the battery was dead again. I put it on a slow charge and in two days the battery was fully charged. The starter was turning at a fast rate. However, it would start (run). I attempted to resynch the keys (these are the original keys) again and it the process did not work. So, I search the internet for a different process. So, I found a different process that required me to press the unlock button five times (Five Times) and put the key in the ignition and place in the on position and press the unlock five times then move the key to start position to crank the car. Now that worked and I drove the car around the block. I turned the car off for two minutes and attempted to start the engine, but it just started but did not crank. I tried the Five Time process but this time the car crank but it sputtered while it was running. I immediately floored the accelerator and made it back home.
I let the car sit for a day before attempting any new troubleshooting steps. I wanted to search the web and the forum for clues and suggestions. So, I removed the alarm and discovered the circuit board was bad. Hoping this was my issue with the battery not staying charged. However, the battery has not lost any voltage since the slow charge. The starter turns but the car will not crank (engine turnover--runs)

Steps taken:
1) replace all batteries in the Fobs
a) The lock and unlock buttons work
b) The light on the dash flashes with I press the buttons
2) Tired to resynch the keys as per instructions by Pizzaguy---after the engine sputtered episode
a) No success. The starter turns but will not crank
3) Pull the RCM and check all solder joints.
a) took to electronic shop to have all solder joints inspected and they discovered only 3 loose solder joints
4) Put RCM back in car
a) car will not start--Starter turns but will not crank
5) Replace the Crank and Cam Sensor with all Bosch parts
a) Car will not start--Starter turns but will not crank.
6) Unplugged the battery and remove Fuses 35 & 37
a) let sit for 3 days
b) took the positive cable and clipped it together with the negative cable (The battery is as not connected)
c) put the fuses back in, reconnected the battery, attempted to resynch the key fobs
d) starter turns but will not crank.
At this point I do not know what to do. There are no import shops in my town and the closest shop is two hours away and they say they have not been successful with this issue in the past.
Looking for suggestions. I am wondering if I should pull the SKEEM, Keys and the ECU and send it to "Mercedes Swamp Shop"?
Any suggestions will do.