When you turn the camera on, before pressing the shutter button at all, do you see an image on the screen, or only black?
If black, shutter potentially damaged.
If image, shutter is open (it should open when turned on, because, mirrorless
) and there something else going on.
Check in the menus,..
Page C-3, item 16, is that set to 1 or 2 ? If set to 1, it may not work with full manual lenses.
Page C-2, item 10, if set to Focus Priority, the shutter may not open when the button is pressed.
Page C-2, item 12, may stop it from opening if the flash hasn't recharged.
The numbers on the bottom of the screen will flash Red if you're below the correct exposure levels.