I'd clean up the wounded area, get some heat shrink tubing, splice in any length required to repair any length lost due to the rubbing & just fix your screw up. For the cost of the parts, you can get some soldering equipment.
How many wires are there? If you do have to replace a connector, ever, & you dont want to spend the $$$ for a factory unit, go to a junkyard & get a connector out of a car & splice that in. If its just 3 or 4 wires & you need a flat connector, a trailer connector will work.

Well, I think yall are absolutley right.

Also Why does it look like ther is gravel embedded in the bottom of the ignitor box?

If some one could help me I need to know which colored wires correspond to which prongs on the ignitor box. When the plug was cut off by the belt most of the wire insulation went as well.

Check that link I posted above. Make sure all contacts are clean and tight. I had problems when one of them was apparently loose.
Perhaps you shorted it when the belt cut through. Check fuses first. And make sure you jump the battery to a car during testing. Lots of testing (cranking) will kill yours quickly.