I have Pistoliers, Shrine to Taal and three developments in my kingdom. Hidden Grove is in play, and I have no developments in my battlefield.

At the beginning of my turn, Pistoliers (normally 1 power) gains an additional 3 power from the Shrine, for a total of 4. At some point I spend a resource to move them to my battlefield. Due to Hidden Grove, they lose all power. Then I put a development in my battlefield.

If it's correct that Hidden Grove doesn't affect the Pistoliers anymore now, do they now have 1 or 4 power?

(If you want a scenario that makes more sense, let's assume my opponent moved my Pistoliers before my capital phase.)

They have 4 power. Both the +3 power and the "lose all power" are non-triggered constant effects. This means they always evaluate and the net effect is applied. So while the Hidden Grove effect is active, the units power is set to zero. When that effect is no longer active, they regain whatever power value the remaining effects would indicate. Basically, the "lose all power" effect on Hidden Grove doesn't actually remove other power effects from the card, it just overrides them as long as it is active.

I see, thank you.