When the non working situation: measure +5v on one RAM chip onboard (pin 8-16), one RAM chip at the expansion board, on U25 (this is at left bottom corner, pin 10-20), and on ROM chip (pin 14,28).

-On the one of the RAM chips (U10 and U14) i have 5v but some times also 0.10V on pin 8 and 16 (most rights pins?)
(And i notice that the screen is not always black but sometime flicker color lines
-On U25 most right pins (10,20) i have 5v
-On the ROM chip (I think you mean above the Z80 i have on 14 and 28 (also most  right pins?) 0 Volt or sometimes 3V

(all in a non working situation...)

seems that the power is not stable ?

Are you measured on the marked pins?

If yes, and no 5V, then I think problem with the 7805 power regulators. Check the pins not are broken, check the solder points. If no any then try to replace these.

Now it is looks problem with the video +12V. Check it on U35, yellow GND, red +5V, blue +12V.

If the +12V only at about 9V, then TR2 are dead. It is can dead when previous problem with +5V. Also can be dead if C9 capacitor dried out. (But Your board have the better type capacitors, the C9 problem usualy with board which use Philips capacitors.)

Could it be a problem with the NICK chip or its power supply ?

About the power supply: this is why i suggested check the +5V at different points, for check both +5VA and +5VB are working.

I think at this point need scope for check Nick signals.