Pictures would help. But what you describe is also confusing.

When you say you have "pressure" when you prime it, do you mean you're getting a pressure reading on a gauge or you're seeing oil flowing from, say the rocker holes? What are you using to prime, a simple shaft, or a stripped distributor? And when running are you viewing the same pressure gauge?

Since you say it runs, we'd have to believe your distributor gear (which drives the pump shaft from the bottom of the dist via the gear on the camshaft) and cam gear are engaging properly. And since you've witnessed "pressure" that says the pump is pumping oil. So, once you fill in some blanks we can start looking at other things.