Hello and welcome to 2CarPros. I've looked up your issue on AllData and the only tests that are suggested there would have to be performed at the Volvo dealership, using expensive proprietary machinery and such. So that won't be much good to us.
What I do know though is this: (1) The keys in these cars use a cr2032 battery (aka a disk battery) which needs to be strong for the immobilizer system to get the proper code from the key. Change that battery. (2) If that doesn't do it, try getting under the hood and inspecting the starter for corrosion (greenish whitish powdery gunk) on it's connectors. If you see any at all, take off that connector and clean it off using a wire brush, piece of sandpaper, or something along those lines.
(4) You'll also want to check every fuse that you can find. See the attached images for fuse box locations. And here's a general guide that we've prepared:
https://www.2carpros.com/articles/how-to-check-a-car-fuse
Start there and good luck to you! Thanks for using 2CarPros.
Harry
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Tuesday, March 12th, 2019 AT 5:19 AM