I have the exact same problem with my 2005 neon. Up til today when i disconected the positive cable it has reset the check engine light and it would run fine for a few days. Now it wont reset and the tone code it 51 the check engine light also blinks 9 times and then stays on the tenth blink.
my battery cables were all cut up and it was raining and the car just died cause the eng mod fuse...
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my battery cables were all cut up and it was raining and the car just died cause the eng mod fuse blew so i changed the battery cables goin to the starter assuming it shorted out and the car started but when i went to go take off the fuse blew again and the car died again and now the same fuse blows everytime you turn the key over what is the problem here