the car starts and runs when hot wired .
this means the start path from the ignition switch to the starter solenoid is defective (open).
if it starts and runs , the battery is good as is its connections.
if it were mine, id put a volt meter on the coil (solenoid) side of the
clutch switch , turn the start key and see if i get 12vdc.
a 12v light bulb could replace a meter, here.
if I did, I would trace this bronken wire to the soleniod, if not id move my
meter to the ignition side of clutch switch, if it failed id move back to t
the ingniton switch.
it is common for Ignition switches to fail , especially with huge key rings full of heavy key sets ( really bad).
1 Ignition sw. (try wiggling the heck out of it)
2 clutch switch
3, bad wires or connectors.
again the car starts and runs when hot wired !
Flash, meter for sale at HF for $2.99 , now anyone can afford it.