Looks like you got a pretty nice '73. Here are a few things you may want to do.
1. Check compression to make sure engine is sound.
2. Check to see if fuel is getting to the SPICA FI pump. Also make sure there's a drive belt to the pump. No fuel to the pump = clogged filter (unlikely) or bad inline fuel pump (most likely).
3. If fuel is getting to the pump, then check to see if fuel is being pumped out. There's a solenoid on the SPICA pump for cold starting. It's the one that's furthest from the drive cog and closest to the fender. Check your spark plugs after 5 no start cranks. If they're wet, dry them out and then try again. IF they're dry, then you don't have enough fuel coming in. Try some starter fluid and see if you can get her to start.
4. Do not crank, crank, crank to start the car. You'll overheat the starter.
5. If you have fuel, then check the spark plug. Make sure you have a spark going to the plug. Check at the plug, then dist cap. If all is good at the plug, then it could be a timing problem. If nothing at the dist cap, check the coil and wire from coil to cap. Check points - they're hard to change on this car - many recommend removing the distributor, so you have easy access.
6. If the battery is low, you may not be able to start the car. My '74 needs a strong battery to start her up.
7. You can start your car with the air cleaner removed. I recommend this method first, so you have access to the SPICA pump and the fuel pump relay.
You should get her to start. She may not run, but at least you'll get a start, which is a good thing. Diagnose the problem, isolate the culprit and change the part. If the SPICA is working, you may want to leave it alone and enjoy the car for a while before changing to the dual DCOE webers.
Put her up on the lift and check for rust at the rockers (inner and outer), wheel wells, fenders (behind the tire), rear quarter (in front of the tire), floorpan, spare tire well and front and rear valance. Look for patch jobs and make sure any repair work is sound and there are no leaks (or you'll rust again). Make sure the drain holed on the rockers are clear.
Check the rear trunion to make sure the rubber wafers are in good condition. Change if they're not. You'll feel the rear end moving if they're worn or missing.
Check engine and transmission mounts to make sure they're okay.
Change all fluids. Check brake hoses (rubber ones) and replace if cracked or brittle. Flush old brake fluid. Check radiator and heater hoses - replace if cracked. Check radiator overflow tank for leaks or cracks. Check radiator cap - make sure it doesn't leak. Change SPICA filter. Change air filter if needed. Replace vacuum hoses and four intake hoses from air cleaner to throttle bodies if cracked. Clean out oil separator (round thing on fender with hoses going to it). Replace hoses as needed. Change transmission fluid and rear diff fluid. Check distributor cap (no cracks and clean on underside with shiny metal contacts). Check rotor (not burned/pitted). Change plugs, unless they're like new condition with good crisp edged on the center electrode.
Check tires (not too old or cracked). Check brakes (lining okay).
If all is good, then enjoy your new Spider. It's convertible season!!!