With the camera on try shining a flashlight at an angle close to the LCD screen and check if you can see any images at all, menus etc.
They will be very faint, so trying this in a darkened room may help to see them.
If you can see images then there's a backlight problem with the screen.
Either on the motherboard, the flex cable connection between the screen and the motherboard (loose?) or the screen itself.
Here's the service manual for the camera and also the ifixit Panasonic Lumix DMC-G7 LCD Panel Replacement guide that may help.
Unfortunately neither has a detailed wiring diagram for the camera although the service manual has a wiring connection diagram - see p.66, but the backlight power is fed to the screen on the smaller 2 wire flex cable as seen in the image from a supplier of the LCD screen.
If it is determined that the screen is the problem, the screen cannot be repaired, it has to be replaced. Search online for Panasonic Lumix DMC-G7 LCD screen to find suppliers that suit you best.
Was the camera described as "fully working" when you bought it or did you manage to try it out first before purchase? If yes and no, contact the seller about the problem and negotiate a new price