2001 Mercury Sable Car not starting

By "doesn't start", I have to assume you mean the engine cranks fast enough to start but it doesn't run. If that is not correct, let me know. "Doesn't start" can mean a lot of different things.

The better approach is to monitor the voltage going to the fuel pump, or to bypass the fuel pump relay to allow testing in the circuit. We never throw random parts at the problem. The easiest way to bypass the fuel pump relay is to pop its cover off, then squeeze the movable contact. At that point the circuit will be live for troubleshooting without having to be cranking the engine or even turning on the ignition switch. The relay is in the fuse box by the radiator.

You should hear the fuel pump running. If it's not, look for the inertia switch in the right side of the trunk. It will have a pair of pink / black wires. Check for 12 volts on both of them. If you do find 12 volts, a failed pump is a good suspect, but we should check for a bad ground first. If you don't find 12 volts, we'll have to work backward to see where it's being lost.