I have an '05 Cooper S cabrio.

Ok, so my check engine and dsc lights have turned on and the car hesitates when starting. I checked my F3 fuse and sure enough it was blown, after replacement it lasted about a mile before blowing again. While the new fuse was in the car started up normally.

I checked for codes and am getting: P0445, P0340, P0031, P0037.

Also, if I hit the accelerator too hard the EML light comes on and I loose power. My AC is blowing hot air, I'm not sure it's related but after doing some searches on this site I thought it might be.

Any ideas as to what could be wrong?