The key inside the battery has nothing to do with its ability to START the car. EWS is the immobilizing system...and it is self powered thru induction. A signal from the EWS control module is sent to the Ring antenna that powers the EWS transponder inside the key.
The battery inside the key is utilized to power the two other features/systems that the remote key has...and that is FZV (remote central locking) and DWA (anti-theft alarm siren system).
The battery inside the key powers the transmission of a 315 MHz radio frequency (in North America) or 433 MHz in Europe) that is picked up by an aerial embedded in the rear left cargo window (on SAVs & Tourings) or the rear window on sedans. That signal is then sent to amps in the C or D pillars (on sedans & Tourings)...or top section of the tailgate on SAVs...then onto the GM where commands are sent to lock/unlock & arm/disarm the vehicle. Don't confuse lock/unlock & arm/disarm (FZV & DWA) functions with EWS. All 3 systems are independent of each other but do work in conjunction with each other.
So if you are having issues starting the vehicle...it has NOTHING to do with the battery inside the key. You may either have an EWS issue or signs of a failing electronic ignition switch.