Hi,
I almost sure to have mislead myself, putting sometimes while programming 16F628 pic in the wrong socket: dip18A instead of dip18B . Thanks for reminding me about the easypic4 setting rules before programming. For the 16F676, I forgot to adjust the JP3 and JP4 jumpers to select dip14 socket .
Besides, I have seen for sure that the breadboard has some problems.
Shifting the whole circuit a few rows up on the breadboard solved the problem with the 16F628, once programmed .