I introduced Linux Mint to a friend to escape Microsoft and apple. Installed Mint 19.3 FBCE on his VivoBook. All works except when the system times out and then asks for a password and will not accept correct password at the login in box after waking system up. Have changed password and now won't accept new password or old one. Have to restart computer. Any help would be great.

Did you actually install it to internal hard drive, or are you still running the live version?
If the latter:

These sorts of password questions have either very simple answers, or slightly more complicated ones.

Simple: re-install, make sure you take note of the proper passwords. Keep in mind there's a difference between user password and root password (the installer mentions this) (most probably only the user password is required).

Complicated: boot into recovery mode and set passwords (most probably only the user password is required) with the utlity. Read before doing that.

I wonder if it's a PAM thing. xscreensaver uses PAM to unlock screens, doesn't it?

I gather from the first post that the password does work when logging in at boot time.

When I installed Linux I chose the option to not have to login with password, I then used Sudo in terminal to change the password it gave the confirmation of the new password so I entered it twice as terminal desired. Now when it times out neither one works. I had him as the only user and admin at install.