I’d look into having the immobilizer reprogrammed. No crank usually means the immobilizer isn’t letting the ecu start the engine. I’ve forgotten if this is the case but I vaguely recall that even hot wiring the starter switch will not crank the starter when the immobilizer isn’t reading the key.
LX or EX?
P.S. When the ecu doesn’t read the transmission to be in neutral or park, it won’t allow the engine to crank either.
If you can get hold of a factory service manual, it would be helpful.
Edit: “neutral or park”