I just installed an MSD Coil in my 2005 MINI. Followed the directions and disconnected the neg from battery. After reconnection everything works fine with the exception of the A/C which doesn't turn on the light and now just blow hot air. I checked the fuses and are OK.

 

Well, it is pretty safe to assume that the coil it'self did not cause the AC failure. Having said that, it is also pretty safe to assume that if it worked right before the install and did not work right after, you did something to cause this.

Take a look around your work area (near the coil) and see if you possibly disconnected a wire somewhere that goes to the compressor or a pressure switch in an AC line.

This is likely going to be solved by an "ahhh haa" moment

 

Kindly check the fuse wheather it is burned out or not, secondly check the relay working or not, replace them if found faulty. kindly check wires are corroded or wires with discontinuity