Not such a strange fault - rather common actually.

There are three functions in the diamond key - one that works with the engine immobiliser system, another that enables/disables the alarm and a third that locks/unlocks doors etc.

The alarm and door unlock are connected but the immobiliser function is NOT related - it is a separate system within the key. This means it is possible for the lock/unlock and alarm functions to fail while the key still works to start the car etc.

Most common issue with key failure is the battery, followed by broken circuit tracks from the key being dropped often.

It may also be that your key has become "un-synced" from the car, although this is unlikely given that a weird combo of button pressed actually unlocks something. Most likely you have broken circuit tracks etc.

An eBay will not work, unless you have access to VERY advanced programming tools.

There are folk that can repair these keys (in the USA anyway...)

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)