[39ClevoUte]

Before you get excited... The wire from the solenoid is there to bypass the resistor or resistive wire. eg: in the some Cars the coil is actually 6-9v and the resistor takes up the difference, then when starting a "full" 12v is put straight to the coil to give it a kick in the guts, in reality it's propably getting it's original 6-9V, but without it it would probably get 3-6v.
If you have an electronic ignition then you should have it connected to 12V whenever the ign is on. You obviously must have a resistor or resitive wire or the broken wire would not have caused a problem. The solenoid wire should be obsolete.
Take the positive wire and any other wires on the + side of the coil off, hot wire the coil. Now try to start the car. It should start fine. This will prove if you have the resistor.