This is a reference post, for search engines, so anyone else who has similar problems might save a bit of time and hassle. Thanks to Jase2985, ratsun81, mentalinc, and the others in the community who helped me work this out.

Symptoms

A New Ryzen 5000 series (5600X 5800X 5900X 5950X) computer with a Gigabyte Aorus B550 motherboard (probably applies to pro, pro v2, elite, master, etc) will not boot. Nothing shows on the screen, and the power button won't turn the computer off. The fans all run, the RAM LEDs go, etc. The RAM light was lit on the motherboard but the CPU light flicked on for a fraction of a second every 20 - 30 seconds - these LEDs are me this was near the RAM, labeled CPU/DRAM/VGA/BOOT on p14 of the motherboard, search for that in the manual.

Diagnosis

The BIOS is not up to date.

BIOS Update Process

 

1. Follow the standard instructions here - format a USB drive (older seems better), format FAT32, download the CORRECT BIOS from the Gigabyte website, unzip it, rename the file to GIGABYTE.bin, copy it into the root folder of the USB
2. Put the USB stick into the CORRECT port. The back panel of the motherboard is misleading, have a look in the motherboard manual which ports is labeled "Q-Flash Plus Port".
3. I left the CPU in but took RAM out, because I had a RAM light flashing. I suspect it works regardless of what is installed.
4. With the computer turned off, hold down the QFLASH button on the back panel then push and release the main power button to turn it on. Leave the Q-Flash button down until you see an orange flashing light on the back panel beside the Q-FLASH button, you can see it from the inside of the case as well. Wait about 5 - 10 minutes until it completely stops flashing... completely stops, not just slows. It eventually completely stops.
5. Turn the computer off. Put any hardware like RAM / disk / CPU in. Turn the computer on. Hit Del to go into BIOS and load optimised defaults. Save and exit.
6. Insert your Windows 10 USB key, install Windows - or other OS of your choice.