I'm assuming it's an OLDS 350. Is the 350 all stock? Rebuilt?
Oil level ok? No metalflakes in the oil? I'd start by popping off the distributor cap. Manually turn the crank using a 1-1/8" (I think it is, IIRC) socket and breaker bar to do it. Turn the crank and if the distributor moves, then your timing chain is at least hooked up. If it doesn't, you probably have a messed up timing chain. Original ones had nylon cam gear teeth that didn't last forever.
If it's a Chevy, do what those guys suggest.
Do you have an oil pressure gage on the car? If not, get one. At least so you can check to see what it is under the hood. The tap point would be the sending switch behind the water pump on the block.
Then, pull the distributor out of the block and see what happens. If no hex rod comes out with it, great. If it does, see if it's broken, twisted, or stripped out on either end.
If all that's good. Make sure the hex pump drive rod goes back into the engine and engages with the oil pump. Then, using a reversible drill motor, set up a 5/16" socket on the end of the hex drive rod and spin the oil pump counter-clockwise.
Watch the oil pressure gage. If the oil pressure still doesn't come up, something is wrong in the oil system.