You should delete (from this thread) or at least alter that Belarc report you have uploaded.
It shows your Windows 7 Home Premium license key, which you don't want broadcasted to the world--which is what you have done by posting it here. It's useful to thieves.
The Belarc report says the SMART status of your hard drive is healthy---that's good, but not conclusive about your hard drive.
At this point, you could have hardware problems or software problems. We can't tell.
You could try another recovery from your recovery partition. If you have failed with it before, it may fail again.
Greg's link will show you how to do a clean install. That would get rid of the HP stuff on your PC.
But clean installs or recoveries are not going to cure bad hardware. Nonetheless, I'd try one or the other.
What specific hardware testing have you done?