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OK so I've got the new key. The car started at the garage and they showed me it doing so several times. It's home again and I'll try it again in a while. My level of confidence has gone up but it's still not 100%, not least because they didn't seem to know what exactly the problem was although they assume a damaged transponder in the old key. I'll let y'all know later.
Car still working today. Why am I hesitant to declare the new key a success? Don't know really. After a couple of weeks of big hassle and probably over a hundred failed starts, each time I turn the key I somehow expect it not to work. But it looks like it's fixed.
This is the OP's original post. Since then good parts have been replaced without proving they are bad. And of course a wallet is getting much smaller, a brain is getting more frustrated and the problem still not fixed. What has not been mentioned - is a discussion of scanning the car with an appropriate scan tool, preferably VIDA. That would be the first step, not guess and replace. Sure test and verify is a good diagnostic process - but antenna rings and usually starters are not erratic and should only be replaced when you can prove they test bad.
What has not been mentioned is the common problem of a water damaged CEM in a xc90. Common failure symptoms courtesy of xemodex.
Now have a problem with the horn coming on (and staying on!) when the car is shut off completely. Have pulled the horn use in the mean time but am beginning to suspect a wider problem. New key starts the car fine and everything else seems to work. Issue with the horn did come after I washed the car though, including hosing with a Karcher (not in the engine bay!) so that may be consistent with water ingress albeit I'm not sure how the water would have reached the electricals.