Dead key

[Paul-R]

You put the working key into the ignition, turned it and then went through the procedure on the non-working key?

[Homer]

Hmmm... Not so sure Paul - this extract (for the X7 at least) would indicate that the Ignition Key Transponder also has some ability to perform a calculation. Probably another reason why the X7 only has the electrical remote fob if this is the case.

First - clarification of the terminology using this diagram:
X7 Ignition Key Transponder.JPG
(1) Ignition key with integral transponder.
(2) Transponder coil .
"a" Ignition key transponder.

But surely it will be powered by induction (hence the transponder coil), not from the fob battery.

Anyway that seems to be proven by the car starting with the fob battery removed.

[Paul-R]

That's for the transponder chip to be interrogated which is completely separate from the lock/unlock mechanism.

Whilst we all agree that ideally the key should be re-paired my contention is that it's not necessary if only the lock/unlock is needed.

Anyway that seems to be proven by the car starting with the fob battery removed.

The battery is ONLY for the lock/unlock. As you say the transponder chip gets its power from the coil.