My problem is solve,
First I waited to go to Genius bar 5th avenue New York.
I explained them my guess was an issue with the internal data cable half out/in.
They told me this device cannot be repaired telling me there are no screw on the iPad.
They proposed to replace the iPad 1 for 240$ without tax as the product was out of warranty.
I refused telling them I was about to open it myself using www.ifixit.com tutorials and tools.
So I ordered the tools recommended by ifixit and I used the tutorial (replace LCD) of course I stopped the tutorial at the time I got acces to the data cable.
I plugged in and out. In and out. Each time trying to startup the device while the iPad was still open just to check that I see the normal grey apple or still the red (bad color) apple .
After 3 attempts I could see the normal grey apple.
That is it