1996 BMW 740 battery

Possibly the EWS will require realignment. EWS is the drive away protection, it is for key recognition, if it can't recognize the key, it won't engage the starter. Some independent shops can do EWS realignment but you might have to go the dealer.

I don't believe, but I may be wrong, you only have to EWS the key recognition when you've lost your key and you have to make a new one. You should have two keys for this BMW, try the backup key, if that does not work I suggest you change the batteries in the keys, insert the key in the ignition, turn it to the on position ( that does not mean start the car) when you have the key in the on position, pressed the big button on the key and hold it for about five seconds let off the button and try to start, if that does not work
after you have done that activate the security system from your key several times, if that does not work, insert your key in the trunk lock and turned to the left that will also activate the security system you should hear the alarm come on and the doors lock, then turned to the right and a locked the car, repeat the same operation on your driver's door

The EWS alignment can be confused by a voltage excursion (like during a battery change) and is not dependent on the battery to function. The battery is for the central locking transmitter. If the keys you have do not start the car, realigning the EWS and reinitializing the keys might be the solution here.

Dr. Hagerty, is absolutely correct, thanks for the comeback.