One other thought re the engine start.
Above I said that the engine start permission does not require battery power from the key fob battery. I think I am correct in that, however there is a contrary view that says the engine start allow circuity within the key fob does need power from the key fob battery.
If you wish to experiment, continue to use the dead key for engine start and see if it keeps allowing start. Also the second key can apparently be charged by either taping or with an elastic band, the key fobs together. The charge field, (as with an electric tooth brush), extends out about 3/4" from the ignition coil so a second nearby key will apparently charge - not pretty but if the charge circuit works, then the second key can be topped up.
The start not start permissions are stored within the CJB printed circuit board and that is why when it goes, it has to be programmed back to the particular vehicle VIN. The actual CCF, Car Configuration File, is however stored or backed up within the Instrument panel pcb so that the new CJB pcb knows where to find its new old data. That in part explains why both are so expensive - both are variations of computers probably running UNIX.
It is good to hear you know of the alternate entry mechanism and that it works.
If you end up purchasing a new key, you can tie the non working one underneath somewhere and you will have your own valet key.