Thank you all people. I still do not know which of the solutions has fixed the fault (I suspect that adding the resistor from PGM to ground was the cure) but... by now I am programming my 18F4620 time after time.
Mister-e: I have never found so smart and plenty of resources guy in any part of the world. Congratulations. Please be patient with people that has an I.C. lower than 150 or 180. In anyway, I thank you all again.
Note: be carefull adding any kind of high frecuency EMI suppresor in series with the supply of the PIC (to avoid the interference generated by the PIC going out to the circuit). At 20Mhz the supply current might be several miliamps. Should the internal resistance of the suppression device is several ohms it makes the 5volts supply to go down while you are programming the part and... you enter in the forum lost like a grape floating in the Atlantic. As I am supplying 5 volts to the PIC from its own board (not from the ICSP interface), the supply was not very clean (I do not know how many miliamps do the pic uses in programming). Do this sound very stupid or can be part of cause in the programming fault?

Maxi.