I have quite a few G7 cameras. A few of these intermittently exhibit some strange behavior where if you press on the mode dial, or in several spots on the back of the camera (where the LCD stores) the mode and the screen jump around rapidly. Popping the back off (easy, but don't do it if you don't know what you are doing) reveals some interesting things. In one corner, and I think this is possibly the problem, there's some small wires that don't quite fit into the clip. They are very thin, so push them into the clip very carefully. Also, be very careful of the ribbon cables.
All of my cameras work perfectly now. After taking the back off, I gently flexed the circuit board towards the lens a few time, reseated the wires in the corner, made sure all the ribbons were in place and fully in their clips, and blew some compressed air into mode dial switch. Not sure which of these fixed the problem, but I suspect it is the wires because some of my cameras have some extra shielding there with a different clip and some do not.
If you do need to pop the back off, make sure to remove the screw in the battery bay and also make sure to remove four screws in the viewfinder. You need to slide off the rubber seal. Again, disassemble only if really needed at your own risk.
When you open the back, you can see that the whole back is a metal heat sink, with a small foam pad in the middle that sits on the hot chip. Inspect that foam as I think it dries out over time if you plan to keep the camera.
To test the (assembled) camera, lightly press the upper right corner of the back where the top of the LCD would go after flipping it out. Try it both in standby and record mode. If nothing happens, leave it be. If under warranty, I recommend factory service over trying to fix it. I suspect there's a design problem that affects some of the cameras.