My own boards works now with the ChibiOS F4 demo, and also with the original ST demo
The problem that it sometimes doesn't work with my own software (based on the Chibi demo) remains, but at least I know that the hardware is ok, so debugging should be much easier now.
I wasted several days searching for a hardware problem was was not there, but it was quite interesting. The micro also runs with wrong or even completely missing decoupling capacitors, the external crystal works without the C's and R. Finally I tried to unsolder the micro from the discovery board. I really put high temperature for a long time on it, but it seems that they use power glue to prevent people from unsoldering (the discovery board has about the same price as a single micro at RS). Even after this torture, it still was alive. So it seems to be quite a robust piece of hardware.
I'll hopefully find my software problem soon...