Original iPhone flashes on and off, DFU won't work

Feb 20, 2012
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I have an original iPhone. When plugged into the computer it flashes on and off (quickly). I am to assume that it is stuck in a recovery loop. I have tried to put it into DFU mode. Problem is that on the screen it asks me to connect to iTunes (when it is open and plugged in) but it shuts off after displaying that on the screen for about 3 seconds. Then I am back to square one. Any ideas?