Your insights would be appreciated.

About a week ago (at an ambient temperature of 103F) and after the car was in the garage for about an hour, an attempt to start it was met by first - wouldn't recognize the chip in the key, second - recongnized the key but a messge of ABS failure, third - a message of brake failure and fourth - no messages, but the car continued to fail to turn over and just rapidly clicked in time with the warning lights in the dash. I let the car sit overnight and the next morning it started without a problem.
I have a simple OBDII reader....no codes reported.

Yesterday, the problem was back. Again, in the garage (at an ambient temperature of 103F) and without any error codes, the engine wouldn't turn over, but would rapidly tick while the dash warning light blinked. This time though it didn't start after sitting overnight, but continuing to cycle the key (and eliciting the ticking) resulted in the car finally starting. At the moment it is starting without problem.

The car has been great for four years and it is about time for some issues, but I would rather not take it to the dealer only to have them tell me they couldn't find a problem or worse, fix something that is expensive that was not the problem. Any thoughts?

Sounds like it might be a weak battery.

Does sound like the battery or alternator. Take it to an independant Volvo dealer, better there than the main stealers.

Where are you based, UK?

US - California

It was indeed the battery - just beginning to fail. I didn't know that if the supplied voltage is even marginally below 12 V, the starter won't crank. What I heard was the solenoid rapidly engaging/disengaging (because there wasn't 12 V). The lights were presumably flashing because of the rapid cycling of the starter.