Hi sharlentouane,
Unfortunately because the above troubleshooting steps have still not resolved the issue, it does appear that the issue is with the hardware. I would suggest contacting technical support at 800-474-6836. If you live outside the US/Canada Region, please click the link below to get the support number for your region http://www.hp.com/cgi-bin/hpsupport/index.pl, for any available repair, or replacement options available to you.
Good luck! :)