Don't just start replacing parts. Diagnose the problem and correct it. Throwing parts at it is no good. Before replacing spark plugs or wires, verify they need to be replaced. You said you replaced the distributor.. Are you sure you timed it correctly? It will run if within maybe 20 degrees of TDC on either side(BTDC/ATDC). I once got a dodge 318 to fire at -16 BTDC which kinda amazed me lol. Because you said you saw it light up a few times on the damper, the coil is functioning as are the wires. So that leads me to believe it's incorrectly timed.
For the 350, 1 is the first piston in the firing order. Piston one is in the front of the engine, on the drivers side. You have to time it with that piston at TDC, on compression stroke. So pull the plug out and stick ur finger in there, while turning the engine clockwise until your finger gets popped out. You should turn it with a nice big breaker bar because using the starter is kinda hard to get it lined up perfect. Once you are on compression stroke, look at the damper and turn it to like 5-8 degrees after TDC(When the piston is traveling back down, so you're gunna go after the mark for TDC(To the right of it)). Then drop the distributor in with the rotor pointing at Cyl. 1. When you put the cap on, adjust it to point at the closest point on the cap, and that point will now be Cyl 1's plug wire spot. Then just put the other plug wires on the cap going clockwise based on the firing order (1-8-4-3-6-5-7-2). It should fire right up even if it's not timed perfectly, it just has to be close. Once it fires, just use the timing light to get it perfect, and then lock her down.