Roca toilet cistern problem

The means of filling is nothing to do with it being a push button operation.

Before delving into it, has it got the usual flexible inlet pipe running from an isolating valve? If so are you sure this is on and that the pipe is not kinked.

Does the lid lift partly - leaving it held by a cable mechanism?. If so then I guess you may need to unscrew the chrome trim that surrounds the button to free the lid from the mechanism.

The ball of the ball valve (or whatever) may have stuck in the up position.

Usually the round frame around the pushbuttons is what retains the lid. It should unscrew by hand.

Ease the buttons off, if they are flush with the surface you may need pointed instrument to help. You shouldn't need much pressure, on mine they are plastic. Then you should see that the collar is held in with a cross-head screw - unscrews and remove top. Be careful not to drop the bits of plastic that the buttons mount on to down the toilet.