1980 C3 Corvette - engine start

Do you have spark?  Do you in fact have gas into the venturis?

Check to make sure you are getting power to the ignition coil.  When the key switch is on, it supplies power to the coil. If the switch it 'messed up' then, possibly it is not properly making the  connection to supply power to the coil.  Looks like there is a pink wire and a white wire....if you have a test light or volt meter, unplug the wire connector and turn the key switch to the run position and see if you have voltage at the pink wire(white wire goes to the tachometer)... if not, then you might "temporarily" hot wire it(splicing into the pink wire with a known 12volt source,not that i advocate "bubba-izing" but sometimes you got to do what you can to get things going)and see if it will start.... then possibly look into replacing the key switch.