Help Fixing Xbox 360 E71 Error? (xbox Can't Get to Dashboard)?

I just got Bioshock 2 for my Xbox 360, so I hooked everything up and put the game in. I got halfway through the opening cutscene, then my Xbox froze. The screen looked like it was checkerboarded. So I turned off the Xbox and turned it back on. Several times. It froze on the dashboard upon trying to move anywhere every time. Finally, it wouldn't start at all, and I got the dreaded Red Ring of Death. I took apart the Xbox, and seeing nothing wrong, put it back together. This time, it gave me the E71 error code.

I've seen that you can reset dashboard updates to fix the problem, but the three methods I've seen don't work, because my Xbox can't reach the dashboard. It just gives me RROD a few seconds after turning it on. Does anybody know another way to reset the dashboard updates without needing to turn the console all the way on?

Suggestion:

Clear Any Failed system updates that cause the console to error.
With the console off, press and hold the sync up button (the small white one)
While holding the sync button press the power button to turn on the console
Continue to hold the sync button until the Console has booted up completely.
During the boot process the console should clear any failed updates, allowing you to use it normally.