I am in the process of building a computer (parts here: pcpartpicker) and I am aware there is an issue with B550 motherboards not supporting AMD 5000 series CPUs out of the box. I have also heard that some motherboards have the correct BIOS version already, while others may need a separate CPU to update the BIOS to the correct version.
Question one is: my system is not POSTing, can I determine if a BIOS version is required vs. other build issues (badly seated wires, dead components, etc.)? Link
And two is: can my current computer's AMD processor (an AMD Phenom II X4 965) stand-in to perform the update on my new computer, or am I better off asking for a loaner from AMD (details here)?
First the Phenom IIx 965 won't fit in a Ryzen Motherboard socket- AM4. That processor uses a different socket - AM3.
You never mentioned your Motherboard's Make & Model. But most Motherboard has either a white sticker with the current Motherboard BIOS installed or is marked on the BIOS chip or somewhere else on the Motherboard.
If the Motherboard you have is manufactured after the BIOS Update that supports the 5000 series processor it should work out of the box. But if it is before the BIOS Update and the motherboard doesn't have a BIOS FLASHBACK feature where you don't need a CPU installed to update the BIOS then you would need to get either a AMD BOOT KIT or find a compatible Ryzen processor that the current BIOS supports to update the BIOS to the correct version to support the 5000 series processor.
Also you need to see if the 5000 series processor you are going to install is supported by your Motherboard by going to its CPU SUPPORT LIST in your Motherboard's Support site.