Car won't start, only clicks rapidly. Some smoke and burning smell

The smoke was coming from the negative terminal wire at the battery. I stripped off some fresh cable, cleaned up the "crimp" part of the connector, reassembled and the car started first try. I think I'll buy some new connectors to head off future issues. Thanks for your help.

THAT'S COOL, but don't buy those crappy cheap 'emergency' repair terminal ends! Go to NAPA and get some real replacement cable ends! They have some that use a compression nut to retain the cable, bronze in color and avail. in diff. sizes. Another option is the crimp/solder on type, better yet but special tools needed to install. You are welcom.