Probook 640 G8 BIOS update screen doesn't appear

[ZK32]

Dear Community,

First of all, I apologize for my poor English!

I bought a refirbushed HP Probook 640 G8 notebook, which is no longer under warranty, and I can't update the BIOS firmware.

Now it has BIOS version 01.02.06, which is the second oldest version, but the "USB-C Controller firmware" (which is part of the BIOS update Softpaqs)  is on the 2.8.0.0 version, which is the level of the BIOS version 1.14.00.

Most of the times the Windows 11 only starts after an automatic reboot. When I restart the Windows, or switch on the notebook, only the HP logo appears, after a few seconds the notebook restarts, the HP logo appears again, and the Windows starts loading (I see the "Windows loading" circle below the HP logo).

All the drivers are updated through the HP Support Assistant, only the BIOS update and the Realtek HD Audio Driver are waiting to update, and none of them disappear after the "Download and install" processes, what I tried.

I tried to update the BIOS with starting the Softpaq from the Windows 11, tried to creating an USB drive from the Softpaq, tried to use this USB drive to start the update from the BIOS "Update from local drive, and tried to upgrade with the BIOS "Update from network" option.

With the first three method the notebook restarts, but the "BIOS update" screen doesn't appear. I see a blank screen with the LCD backlight is on, and the system fan starts to spin quickly, but nothing else happens, not even for several hours.

With the "BIOS update from network" method, after automatic searching the hp.com for the newer BIOS version (still in the BIOS) writes out that only downgrade to 01.02.04 is available. But when I start downgrading, then writes out out an error message that says: there is an error, because the "USB-C Controller firmware" is newer,...

I tried to start the notebook with held down the Win+B / Win+V / B or V keys. I tried to push the power on switch for 20-25 seconds, but nothing helped. The BIOS update "program" doesn't start.

I disconnected the main battery and the BIOS battery and after pushed the power button...

I tried diagnose with the UEFI Diagnostic tools, and HP Hardeware Diagnostic Tool, but none of them showed any error,

everything is OK.

What do you think?

The BIOS / Sure Start chip went wrong?

Or someone updated with a wrong BIOS version?

I read somwhere that, maybe it could be a replaced motherboard, what wasn't setup properly, and should be reopened to setup correctly. According to that suggestsion a should use the BIOS Configuration Utility.

What do you think about it? Would it help me? And if yes, how should I use it?

Can someone help me?

Thank you in advanced for your help!