Xbox 360 error code E76 is an error that usually indicates there may be a problem with your console. It may also be due to a dead working chip.
1. Warranty your Xbox 360
"Xbox 360 error code E76"occur when a mainboard chip is dead. The cause of the dead chip could be a broken solder joint. The broken solder joint may be a result of overheat because solder joints are lead metal that melts to a certain temperature. Solder Joints connects the chips to the mainboard. If the solder joint is broken, the chip may not able to communicate with other chips and other devices result to "Xbox 360 error code E76."
To repair this, send your console to Xbox to a service center if under warranty. However, if the warranty is void or null, try the solution in this link here, or look for a technician that reball or reflow electronic chip.