After a few insightful days and PMs with alex later (of course huge thanks to his help as always) I seem to have figured out the problem with this camera.
Perhaps its helpful for others with similar issues.
alex analyzed the logs and told me
Your ROM boots fine in QEMU, camera starts with main display off, menus in German. So, if there is anything wrong, it must be from the MPU (secondary CPU).
Possible suspect: the power button.Well, I figured out that its pretty simple to get the backside of the 50D off (quiet similar at least to 40D and 5DII), there are helpful videos at youtube. You just have to unscrew 4 or 5 screws, one is under the grip-leather (pretty easy to peel it off). After that just 2 flex cables are connected to the camera.
Interesting behaviour was, that without the whole camera backside, the camera showed all the normal settings on the upper display when the battery is connected again. Also AutoFocus worked fine, but the camera didn't engage the shutter.
Also when I just connected one flex cable it behaved the same way. When the flex cable with the power-switch is connected it didn't start anymore.
So I had a closer look at the power switch. One component is the hardware-power-lever you see from the outside... but that thing is internally connected to a tiny switch on the inside that also has the 3 states "Off / ON / Locked".
Well, the problem is simply the tiny switch on the flex cable which failed or is broken. It doesn't spring back when the camera is Off and the power lever is turned back On.
To clarify here is an explanation-image:

With a tiny screwdriver I can switch the micro switch to on, leave it there, put the battery back in and the camera starts normal again, with LCD image and all the function buttons on the back. Hooray.

At that point its the simplest way to just leave the micro switch and power lever disconnected and the camera always "On" and just shut it On/Off by putting the battery in/out. The micro switch in the battery compartment is kinda my new power switch.

alex added
You'd have to power down the camera by opening the CF card door - which is a perfectly clean shutdown, btw.
Even more - with ML, opening the card door while leaving the power switch to "on" is actually the safest method to turn off the camera. That's because the camera no longer wakes up to read autoexec.bin whenever you want to remove the CF card.My conclusion is ... no wonder that Canon changed the power-switch layout after the 5DII (which should be a somewhat professional camera). ;-) That tiny thing is an essential part of the camera and can affect it to stop working.
/edit
Thanks to Mike Tornado, the specific switch in question is a
Panasonic ESE23J101.