Bios locked with admin password (HP 820-G2)

[Manecik]

My notebook is a locked wit admin password.

My laptop has a broken motherboard, the child spilled coffee. The laptop is working fine now, nothing happened. The motherboard has been cleaned and dried.
Unfortunately, there is an error when turning on the computer.

BIOS error: CMOS checksum invalid, error 502.
The computer will be reset and the BIOS settings will be reset to standard.

Then the classic system boot follows and everything works fine.
Another thing happened, namely, the computer was protected by a BIOS administrator password. I know this password, my ADMIN password, but it doesn't match. It was always like that, no one changed it. The system says that the password is BAD.
Additionally, the computer itself changes the time and date.

I've tried all the tips and tricks available on google.
Updating the bios is impossible, you need to enter a password.

I need the SMC.bin file but I have read that HP does not provide these files anymore.

A motherboard in my country costs half the price of a used 820-G2.
What I should do now?
Is it worth writing and asking HP to make an exception?

This is my fourth Elitebook in my life. There have never been problems with HP.

My BIOS is not fully locked, I can boot PENDRIVE and my operating system. USB ports are not blocked.

Why is my password no longer matching ??
Sorry for the quality of the english language.

[WAWood]

@Manecik 

Sorry, but you've already done considerable research and answered your own questions.

HP does not reset BIOS passwords and as you have found out, will charge you to replace the motherboard.

And no, HP does not make exceptions because if they did, then EVERYONE would claim to be an exception.

If your PC reset your password on you, we can not help in that because we have no access to either the original or the new password.

We are not permitted to assist in resetting passwords because HP considers that a violation of customer privacy. HP can assist in resetting passwords but if your original warranty has expired, they will charge you for the assistance.

[Manecik]

I have proof of purchase of the motherboard, I am the owner of the computer. I also have all the data like UUID and so on. I read that exceptions are possible when a complete set of documents (identity and hardware purchase) is sent to HP.