DragonFlyBSD

Correct. I also noticed that when the login prompt is put on screen, the
num lock -indicator (on keyboard) is on and right after I try to write
something, the light goes off.

I meant that OS freezes ONLY when ACPI is enabled. The issue was that I
wanted to use single user mode and when I choose it from menu, system
freezed then too and I didn't know how to get to single user mode with
ACPI disabled, but now I do. ;-).

(1) So you want me to do the following:
1. Select 6 (Escape to loader prompt) from menu,
2. type boot -v ENTER and
3. reboot (from freeze) and send the content of dmesg to you?

(2) Isn't the content of dmesg ONLY from latest boot?

Keyboard works fine when option 6 is selected. ;-)

EDIT

(3) Does /var/log/messages adapt to your needs?