Is there any way to test the key fob function for my 06 R53?

None of the buttons work, it was operating fine a week ago. I'm assuming it is just a dead battery, but I don't want to spend money on a new key only to discover that the issue is on the receiver side, rather than transmit side.

I don't have a second fob to test receiver function.
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Probably a dead battery. You can try to pair the key to the car as a test. Look on YouTube, it’s a 1 minute process you do at home.

if that doesn’t work, email MINI Key Hospital at minikeyhospital@outlook.com He can replace the battery and save you the cost of a new key from the dealer. You’ll be without a key for a week.

Or, since you only have one key, maybe just bite the bullet and get another one made through the dealer.