i would almost bet it is a ground problem where it will pass high amperage but not low, kind of like a situation where a digital volt/ohm meter will show power but an old fashioned test light won't light up. if you have not done so i would clean all the grounds i could starting with the easiest ones on the battery first. i also would get a good cat in case it is mice damage so it does not get you again! like the visa commercial says...... "cat food 14.99, a barn cat chewing on a mouse priceless".