Fuel pump relay

I do not have information for your car brand, but I can suggest a couple of things. First of all, there had better not be power to the fuel pump when the engine is not running. You will typically hear the hum of the pump or find voltage to it for just one second when you turn on the ignition switch, then it will go to 0 volts. That voltage should return any time the engine is rotating, meaning cranking or running.

On the majority of car brands, the majority of crank/no-starts includes no fuel pump, no injector pulses, and no spark. Too many people get hung up on the first thing they find missing, so check for spark too. If that is missing, the most common suspects are the crankshaft position sensor and the camshaft position sensor. If you have access to a diagnostic fault code reader, start by reading the codes. Those will indicate the circuit or system that needs further diagnosis. If there is no code related to either sensor circuit, you will need a scanner to view live data and see if those sensors are listed with some indication as to whether their signals are showing up at the engine computer.

Have you checked for spark?