I'll bet the starter relay has failed.
Have someone hold the ignition key in the "start" position and check for voltage at the yellow wire. If you have voltage there, it's the relay. That's not an uncommon failure.
Ballast resistor and fuses have nothing to do with this.
You need to fix this ASAP. It's dangerous and quite frankly, there's no good excuse for not having it in place.
That said, the relay must have that terminal grounded some way. The relays built for manual trans cars have a tab that grounds to the case. The case then grounds to the body. If that is the case, check for proper ground. If it's jumper wired to ground some other way, check for ground at those connections. IMHO, if the person that sold it to you had it configured that way, everything is now questionable.