If the LCD screen is black, it sounds like the DIGIC-8 processor is not fully running. The LCD should illuminate even without a SD card installed when you press "Menu". Can you see any of the exposure or mode info in the optical viewfinder edge displays? Since you can't access menus a "factory reset" is not possible.
If you're sure you have a good battery installed, you might try this as a last resort before contacting Canon Service (1-800-385-2155):
1. Remove the battery and SD card.
2. Switch the power switch to "ON" and fully depress the shutter button for 10 seconds. Then depress and hold the -> image display button for 10 seconds. That can sometimes clear stored register errors.
3. Re-insert a known good battery and wait (don't touch ANY controls or buttons) until the red light stops flashing.
Also, have you looked inside the mirror chamber checking for a mirror that has not returned to it's normal location or a partially jammed shutter leaf? If the mirror is down, then it's impossible to check the shutter leaf positions or to check for anything caught in the shutter. Good Luck
