Very true on the filter being mounted backwards, I forgot about that. Thanks Leegrady. I suggested "priming" the system since that would lead the OP to find if there was possible dirt in the line and/or any air, but again, you are correct on the air not causing a vapor lock. The OP did check the pressure at the line I think as posted above.
Its probably a FP relay, fuse or the pump itself, but it does not hurt to try the cheapest and easiest ways first as you stated, the Fuel filter might be backwards, but the OP says he is not hearing the pump at all, and he is getting no pressure at the filter either. So I suggest that it is not the Fuel Filter since he would still have pressure at the inlet side of the filter, and he would here the pump.
I very much appreciate the civil, and non-egotistical way you wrote a reply to my suggestions. Thank you. We are on the same page.
At this point, if there is no pressure at the rail, and no fuel at the inlet side of the filter under pressure from the pump, and not just siphonning out, then the pump is not working.
The question then is it really a defective pump or caused by error in the heater core replacement causing no power to pump.
Check for battery + at the fuse. If there is no power there I would work my way from there toward the dash, and also run a test lead, with inline fuse built in, to power the fuel pump directly. Same with the relay. Follow a wire diagram, because I'm just hinting to help keep thing moving to solve the compaint.
Another reason pumps are in the tank is for quiet operation. On my '95 T-Bird 4.6 I hear a whirl sound when I turn the key on. But that's about all I ever hear of the fuel pump. If that whirl sound is the pump, and not something else. I'm not sure.
I will add that air in a fuel line, and vapor lock are technically two different things. Vapor lock occurs from gasoline boiling from a heat source.