'05 Limited Convertible, when I went to start my car this morning the engine turned over for 5 seconds or so but would not fire and crank. I normally wait for the fuel pump noise to stop before I start cranking, on my first try I thought I just didn't hear it start up. But after the failure to crank I tried again and it was definitely missing.

I pulled the RCM and looked at the solder joints thinking this was a mystery no start. However, they look pretty good, have a negligible resistance from the backside to the front side. I then plugged the RCM back in and had someone turn the key to the on position. The relays snapped closed to complete the circuit, but there was no noise for the fuel pump (there was a fan noise that started up). I had them then try to crank and once again it just turned over for a few seconds before shutting down.

I've read on here that the fuel system needs input from the crank shaft position sensor and cam shaft position sensor. If either of those were bad I would not expect the relay to snap into the closed position. Is that the correct way to think about it? Right now I'm thinking I've got a bad fuel pump. How can I verify before purchasing and replacing?

Prior replacements as follows:
Camshaft PS - October '18
Crankshaft PS - August '15
SKREEM - October '18