Happy new year!
@Miti: It's a bit too late for Christmas spirit, maybe it will serve as a rather expensive christmas light this year, but I would like to prevent this from happening.

If it got it right, the idea is to heat up or cool down the flash memory (need to check, where it is actually located) while booting and hope the red screen will go away and then try to reflash the memory via USB with a special key. Do you have any information regaring this special key, where can I get it?
@Adrian_Arg.: Unfortunately I have already tried both potential fixes, the factory reset with the 5th button did not work, there is no change, if I repeatedly press it while powering it on. The mentioned reflash option with a USB drive and pressing the HELP did not really work out, the scope is definitely doing something but I can hardly interpret the feedback of the scope. CH1 led starts to blink for a couple of seconds and after that all leds will start to blink as well (including annoying beeping sounds). I assume, all leds blinking indicates a failure state, but I am not so sure about it. I tried it multiple times now.
This is actually as well the option mentioned on the Rigol homepage how to fix the red screen issue.
I noticed that it should be possible to flash the memory via Ethernet, I will try to establish a connection with my scope that way. Actually, I assume that the boot sequence gets actually completed, which means I should be able to communicate with a scope via USB or Ethernet.
Thanks.
Regards