If you've got an new-ish in the last year sandy bridge laptop with switchable graphics this a is known issue with HP notebooks. Basically when you turn it on you'll get the HP logo then black while it appears as though the notebook is running. It has somethign to do with the power settings and the notebook trying to use the wrong GPU (integrated or discrete) during startup.
What you'll need to do is hook up your PC to an external monitor/tv via the HDMI or VGA out. Boot the PC as normal and then open up the "Configure Switchable Graphics" menu by right clicking the desktop. Then select use "Low Power Graphics" and uncheck the box that says something like "Use low power graphics when on battery automatically". This usually stops the problem from ocurring.
had the same problem for a few days. found that having usb hub and a verizon phone connected (for charging, no software added) was locking it up on HP screen. would eventually startup after hours when i left it alone . Ok now with usb hub disconnected. I will plug phone to wall to charge from now on.