i just got a 2003 rx300 and it cranks but doesnt start and says no communication with ecu on a scan tool and only half of the dashboard lights come on.
but if you smack the efi relay all the dashboard lights turn on like they should when you first turn on the car. and the car starts up just fine.
i have tried switching the relays and it still does the same thing. i looked at a wiring diagram and the efi relay also supplies power to ecu. but once the car is running it runs fine its just when you turn the car off you have to pop the hood and smack the relays to start up again…
it used to start up just fine but one day i plugged in a cheap code reader with the engine running and i unplugged it with the engine running and then i went to drive and the abs light was flashing and i parked it and then it cranked no started untill i started messing with the fuse box and it started again.
im not sure if that is just a coincidence or if the wiring underneath the fuse box is loose or something?

 

That would seem to eliminate the relay. How about the wiring/connectors?

 

Could be a loose ground .. specially if some work was done [there is the infamous hidden [not visible] ground on the firewall]

Salim