I believe I tore the EWS charge coil when swapping the battery out of my R50 3-button key fob. Am I screwed? Car won't crank/start and I don't even get the continuous beeping noise when I put the key close or in the ignition. I have another R50 with keys that work to compare.

 

Key was screwed. Had to order two replacements on Ebay. Went to a local locksmith to cut the keys $20/each. Bought the AK90+ key programmer for first-gen MINIs off Ebay for $25. Downloaded the software on Windows XP and Windows 7 machine. Got two new keys for less than $50!