I think Jac Mac has it. But it could be you have the "only while starting" side of the solinoid connected to the box. If you have a two stud solinoid, one side allows you to by-pass the coil resistor for hotter starts. The problem is it turns off once you let go of the key.
May I suggest a check of the solinoid wiring before you get deeper in.
Additionally, grounds are a big issue. Make sure yours are all making good contact.
Just my $0.02 worth.
