I don't understand why the battery in the remote could cause it not to start. ?
Correct me if wrong, but surely the chip held in the key contains all the information needed. With a flat battery in remote, the correct key/chip, would unlock manually, and when turned in ignition would start. Assuming every thing else ok, correct key with correct chip = unlock and start. ?
If you were out in the desert and the fob battery went flat with no replacement handy, you would be stranded, if that was the case. Ecu and fuses suggested by others earlier in thread.