normally you have to tell the cars ecu that this is the key you want to use as far as i know you put the key in the ignition turn it to the first position then hold the button on the fob this tell the car that this is the key to use i think that there is a video on you tube for this hope this helps
Does your car have aircon fitted? Maybe the motor noise is the recirculation flap being activated to stop exhaust fumes from being drawn into the car just after it has started. This happens especially when you are reversing out of a garage or onto a main road. It's the recirculation Flap/Motor. At worst case you will need a complete air box to fix it (if the flap stop pin has broken). Also you have a stepper motor that could have a broken linkage arm on it its probably the left footwall flap or blend air flap.
The refrigeration system in all vehicles should be repaired by a certified HVAC technician or equilavent. Dealing with R134A the refrigerant used in your vehicle is dangerous. The electrical checks to determine the repair are difficult and depending on what the problem is are costly and may involve removing the refrigerant with special machinery
to replace a sensor or major item in the system.
Lastly in most states its illegal to purchase refrigerants and /or render repairs on a/c systems without the proper certifications.
In your case it appears that the blend doors or blower motors are not working because you stated in your write up that compressor is on and refrigerant is a-ok.
Have a technician check this out. May have to remove dash board to do testing. This is money well spent.