Debugging would be much easier if you had more than one key. I know the new BMW diamond keys cost $$ but ...

could you borrow a diamond key from someone and try to program it? If you were out here in CA, I'd gladly let you borrow one of mine.

Have you considered buying a new (non-BMW) or used (genuine BMW) key fob on eBay? You are not likely to get the EWS (immobilizer) portion to work, but the keyless entry should be programmable. For around $15 you can get a used genuine BMW key that should be programmable. If you find that can be programmed, you will have found that your key fob has a problem. If you find the eBay key cannot be programmed for keyless entry, you will need to decide whether the problem is with that eBay key or your car. Not a perfect test, but might be helpful.

Having bought 3x used genuine diamond keys off eBay when I first got my E53, and later done some surgery on them to replace batteries in two of them (postings on here if you search on my username), I'll say that they are amazingly well built. Looked like new when opened up. The batteries should last up to 20 years, so yours at 6 should be fine, but maybe it is not being charged. There is a coil surrounding the ignition cylinder which provides an RF field to charge the key's battery. Maybe something is wrong there ???

A problem I once had on my car (2001 3.0i) was an electrical problem with a replacement driver's door lock actuator. Something with that component was causing (I think, whatever I wrote back in the day is accurate, this is from memory) the keyless entry to not work at all; the central locking button would work on the front doors and kind of work on the rear doors, as if they were weak, with failing actuators. I even used my Foxwell to actuate all the door lock actuators repeatedly for testing, and the rears were weak and worked about half the time. Then when I swapped back in my original driver's DLA (which was fine except that the cable bracket was cracked - but had no electrical problems), everything worked perfectly, including those rear door lock actuators.

My basic shock and conclusion was that the whole system is surprisingly fragile with a fault in one place causing symptoms in other parts. Everything is perfectly solid since I fixed that cable bracket and put the original DLA back in - has been for years now.

Luckily when I had that problem, I had an original diamond key and 3x programmed eBay diamond keys (with blades cut off to make them fobs) to confirm it was not a key problem.

So for you - I'd be cautious about drawing any firm conclusions about the health of the central locking system unless everything works perfectly.

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2001 X5 3.0i, 203k miles, AT, owned since 2014