the fuel pump relay must energize for 3 seconds and release every key on. no start.
and when cranking , and when running.
you ecu is messed up. (maybe)
is Check engine lamp , on key on ,no start.
the check engine lamp goes out when rpm exceeds 300 rpm. (however)
if engine starts, CEL must go out, if not pull error codes, running or not with key on.
you can pull codes now. while cranking,
sounds like bad ecu.
or bad wiring to FP relay.
need a schematic.?
schematics to run engine
here.