that's why one should drive a diesel.
so the car ran before replacing that relay?
anyway, does it get a spark? take off one of the sparkplug wires, stick a screwdriver in it and crank the engine whilst holding it close to the block. it should spark.
also, maybe the injectors don't open up. you can check that with a voltmeter, is there power going to them or not?
keep that lip clean, under the airfilter. that can cause difficulty adjusting the idle. but clean in cautious, don't spray blast the dirt inside...
cap and rotor can very well be the issue here. or somehow it's flooded. take out a spark plug and check. (then you can also check if it gets a spark)
the 300e is junk. they have mechanical injection, which sucks and eats gas like crazy.