Unless there was a fire the starter should be fine. Not sure the "mechanic" was qualified. Starters are very simple devices. The heavy wire from the battery is connected to the starter "solenoid" which is attached to the starter. The solenoid is nothing more than an on off switch controlled by a small voltage from your ignition switch. It may pass through more relays on the way but in a simple system it controls the starter solenoid directly which makes "hot wiring" easy.
Replace the burned cable. Look at the small wire or wires on the solenoid. One should go to ground. If only one small terminal the solenoid is internally grounded.
Use a jumper to apply 12 volts to the little terminal while the ignition key is in the run position. It will startle you the first time but should turn the engine over easily if the batteries are still ok and charged.
If this gets it running you can either find which fuse is blown or connect a temporary wire from the little terminal to a convenient place where you can connect 12 volts.