[kooldraco]

stay away from clip kits, they're not that reliable, but if you still want to use it then get a continuity tester and make sure the bios-clip is coming in contact with the chips legs and check that the bios-clip is secure.
Make sure your ground and power wires are as short as possible and the connection is well secure, make sure there are no bridges on “W” or on any of the cd/dvd controller connections.
I had never heard of a blue screen before, just make sure none of your wires are grounding somewhere.
The max payne issue is normal, this chip had overheating issues and lots of games would freeze so to correct that they made the chip turn off right after boot, but there are games that do a double check of authenticity, this game does it after the intro and by then the chip is turn off so it fails and you get the red screen
“inserting a DVD/CD( whatever format ) after the bootup into Bios wont work - just checking for media the whole time in the Browser.”
This is also normal, this chip does not allow booting from browser so you have to press the reset button every time you want to boot a game.
The dms3 is just as good as a messiah2 and it offers a few more features that’s why it costs a more too

If you can’t resolve your issue I would suggest you completely remove the chip and make sure your ps2 works as it’s supposed to without the chip if all is fine then install a better chip or if you want to use the same one, install it without the clip kit.