How about acquiring the AC unit? Be sure you can get a refund if that doesn't do the trick. Perhaps the contacts are dirty. You can try a pencil eraser. This works well with Ram cards so it may solve your issue. Be sure to have an air compressor can to blow out any excess. There are also contact cleaners that quickly dry and clean contacts that may help. if you bought your camera on a credit card your warranty should be doubled as with most credit cards. As far as I know (i've done 3 already) camera needs to be "on" to do the firmware update. Try pulling out the CF card see if the camera turns on.
I had the exact same problem, and the fix was easy. Try replacing the Date/Time Battery (it's a CR1616 lithium battery); it did the trick for me, everything got back to normal. See page 235 of your owner's manual for its location. Good luck!
You may want to update your firmware. I had an issue much like this and they said that they had an update come out to fix this issue soon after the camera was released. You can find firmware updates on canons website.
This is usually caused by a loose screw (one or more of the screws holding the DC to DC board on the bottom). They can end up anywhere and usually cause extensive circuit damage by shorting different parts of the camera. This is a Canon repair
