Oh boy.... Not sure if I can help and only just saw your post.
I don't have a 7DII (yet), so can only suggest things that have cleared up similar problems with other models.
The most obvious thing you have probably already tried... Are you certain the batteries are adwquately and properly charged? During first few uses, batteries may not take a full charge and give expected number of shots. I've also seen chargers not work properly, though that's pretty rare.
Do you have a battery grip on the camera? If so, try removing and reinstalling it. Sometimes I've had a grip get slighly loose and the camera shut down suddenly from lack of any power.
Not sure if the 7DII's grip has an off/on switch, but some of the other battery grips I've used have had one that was easily bumped to the off position, or even in-between the off and on positions, turing the camera off. That's something else to check, if using a grip and it has a power switch.
Have you tried a "reboot"? This involves removing all the batteries, turning the camera on and pressing the shutter release button once (won't power up or fire the shutter, this is just to drain all remaining power in the camera). Then turn it off, put batteries back in and turn back on. If it rebooted properly, you should need to reset the date/time. If not, you may need to leave the batteries out for a longer time. This can clear unknown problems, much as rebooting a computer will do. It likely will mean most or all settings are returned to their defaults, though... so be sure to check anything you had set.
I just looked to see if the 7DII has a user removeable date/time battery and it doesn't appear to. If that's the case, you may not be able to do the "reboot" (aka "hard reset") I described. This is because the cameras without user-removeable button batteries have a semi-permanent battery serving the same purpose, internal and on one of the circuits. These are recharged by the main/rechargeable LP-E6 battery(ies) and provide backup to retain settings, date/time for about 3 months.
Finally check that the electronic contacts lens to camera and the power contacts for batteries are all clean and unobstructed.
Hope this helps! Keep us posted.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7D(x2), 50D(x3), some other cameras, various lenses & accessories
FLICKR & PRINTROOM
