Mikepier wrote:
UPDATE: This morning I removed the well cap, and filled up to the top
with water, then tried the pump again, still water only coming out in
spurts, and not consistent.

I understand I need a check valve, but for the purpose of testing the
pump right now, shouldn't the pump work even without a check valve?
Like I said, I filled up the well pipe to the top, and I poured water
in the outlet pipe, so I'm sure the pump is primed.

If you have a way to apply water pressure to the inlet side pipes, do so while
you start the pump. When it starts to pump, shut off the inlet water and see if
it continues to pump. This will help flush any air in the system.