Ok so here is a positive update...

I had removed my resonator last night to rule it out and got the same issue with the chip's internal oscilator. Today I just put back the resonator and set _XT_OSC again and now it is working fine at 4 MHz.

Furthermore...! if I remove the LCD_Anypin, it is now still working with the standard version.

So please correct me if I am wrong but I am working with a breadboard and I suspect when I had the resonator at first, there was a bad contact with one of its pin!

Thanks to all for your responses, it kept me going.

Mike