My mercury mystique ran out of gas I put gas in it but wont start

You might have damaged the fuel tank and/or wiring and/or fuel pump and/or fuel lines

Sounds like you roached you timing belt. Of course the engine will not run until you replace the belt.

i think you have to adjust the gas cable to a higher RPM usually this is around 850RPM on the dashboard

replace the fuel filter, first, if there is no check engine light, if that does not fix the problem ck the fuel pressure for possible fuel pump failure

Does the check engine light go OUT while cranking? If not , if it stays ON, you've got a bad crankshaft position sensor. These can fail with intermittent no starts. So just when you have it towed it, it'll start working again. Check engine light is supposed to go OUT if it's getting good signal from the sensor.

Fuel in the tank does not mean fuel in the injectors. Run a fuel pressure test to see how much fuel pressure there is. Also check the injector pulse with a noide test light. The injectors may not be getting a ground to fire because of a bad fuse.

More likely you have a worn out fuel pump

Did you put gas back in it and its not running?

MAYBE CATALYTIC CONVERTER STOPPED UP.

sounds like a bad ingition coil