@holger1405
@Jocobai
many thanks for the help for both of you.
Well, I cannot remember 100% sure but AFAICR this error message only started to pop up after the manual installation of patch 1.02. Therefore you must be right that this copied the 2 DLLs into the Binaries.
However I could not start ME1 before the 1.02 install either (it was the main reason why I installed the patch). The only difference was that before the patch there was no error message at all . Actually the exe file behavied very similarly in the memory (I monitored it in the Task Manager) - it has loaded approximately 20 MB. After the patch, after clicking on the OK button in the message window the exe disappeared from the memory. Before the patch the exe simply disappeared on its own at that stage - I guess it terminated itself upon failed verification without any kind of message. I have heard today that yesterday the EA servers were down but I am not sure if it could cause the pre-patch issue. So it was still a weird thing because I think it is a right expectation that a Steam installed game would give a message if an error happens during load.
The learning for me is that I will have to be cautious after the disk install if a problem arises.
Anyway, do not waste more time for my issue now.