Can a fuel pump prime but still not work?

OK, so i figured my starting problem is related to fuel, because i started the car with starting fluid yesterday. I think the problem is my fuel pump.
Heres the thing, I dont hear the pump prime when i turn the key, but if I bypass the relay, I hear the pump make some sort of noise. It doesnt soudn the like loud priming noise, its just a vibrating almost buzzing noise.
Even when I bypass it, it doesnt start. I really dont know what to do, im so close but so far

As we are already dealing with your no start problem in another thread, there is no need to re-post, as discussed in our pm. This post will be locked. Thanks for your understanding.