2 keys 1 ok / 2nd sorta dead
If the battery is dead or damaged inside the key...change it (old style key or new style key)...or recharge it (new style key) by inserting it into the ignition and turning the key to at least position 1 for up to 30 hours (if completely discharged). A dead key battery will interrupt the DWA/FZV functions...but the key should still be able to start the car.
Programming the key Since your 01 should have the new style remote key...if it's not starting the car, but the key fits the ignition and will turn to the start position...there's probably something wrong with the EEPROM inside the key...or it's out of sync with the other EWS components. You're going to need a dealer's help or find an Indy mech or other BMW owner that has the software/hardware to access the car's communication BUS system.
have a set of 2 keys, (just got a used 2001 740iL) appears that 2nd key was never used by original owner ad I suspect the battery is dead or not initialized, will manually open doors, and start engine. First key is OK- does everything properly.
question is... If I follow the the procedure and re-program 2nd key, do I also have to do the same for the first key, which is not a problem