the coil and igniter could possibly cause the shutting off problem and there is an out side chance it could cause the lack of peek power if coil is weak.im guessing the igniter isnt bad and the mechanic is guessing both to cover his ass. as for the starting just take the alarm out of the loop by reconecting the wires to ign switch to see if it starts.if you are going to do the work yourself id go buy the coil or borrow one and start there.good luck