Just because you have a problem, doesn't automatically mean there are lawsuits pending against your unit's manufacturer. Besides, companies would be tied up in endless litigation if everyone jumped immediately to a lawsuit instead of getting their problem fixed.
Is it still under warranty? If so, have you contacted HP? If you have contacted them, what was their response? What makes you think you have a case? Have you connected the unit to an external monitor to see if you have a system board / video card issue or a monitor issue? Have you done ANYTHING at all besides looking at lawsuits?