Your motherboard will accept this CPU but what BIOS version do you have? The BIOS may not recognise the new CPU.
The ASUS PRIME X370-PRO board requires BIOS version 4801, or higher, for the Ryzen 7 3800X CPU. The current version is 5606. If this fixes it then an outdated BIOS was the problem.
You did not mention which graphics card you have. Did you remember to connect the 6-pin or 8-pin PCI-E power connector from the power supply to your graphics card? Make sure the card is seated properly on the motherboard. Take a close look at the motherboard to see if any other connections are not secure.
It might also be a good idea to take out the CMOS’s silver coin battery to reset the BIOS. Unplug mains power cable and press power on button to discharge any residual electricity. Look at your manual for the CMOS/RTC RAM jumper pins. They suggest using a screw driver to short the pins if only two or use the jumper, as shown, when three pins.
The following will only work if you can get to the initial boot screen before Windows loads but if you get to this point you can try booting up in Safe Mode which will load the generic Windows graphics driver. If this works then you know it is a driver problem.
Any how try the above and get back to us in case if it still doesn’t boot properly.
Update: Same topic but different AMD motherboard. ASUS Prime 550M-K ARGB CSM and a AM4 2200G CPU. This needed the opposite to work - it had the latest BOIS/UEFI version 3607 but needed it flashed to the earlier v3205. Why? With v3404 1. Update AGESA version to ComboV2PI 1.2.0.B
2. Update AMD 5000/3000 Series CPU
the older 2200G wasn't seen and the front light flashed rapidly falsely indicating a damaged CPU. Trying it on another motherboard confirmed that the CPU was fine.
Fortunately ASUS allows flashing with an earlier BIOS unlike ASRock which doesn't.