From HP dupport documentation
"Hard Disk Test
Hard Disk 2 Full
The hard disk drive may have failed. Contact HP Support for further assistance."
in common with many HDD manufacturers checks and many OEM checks - HP do not make available what code 306 means
So you may if the computer is within three years of age, contact HP and tell them the symptoms and the results and see how far you go, I say three years because some HDD`s are guaranteed against failure in that time. Although I recently read that many suppliers are now reducing that to one year, See below
I have no idea what code 306 means, but again HP may help you even if not to replace the drive, as I see little chance of this occurring - with you being the second (at least) owner
Please go back to the screen for the options of the tests, run the others offered and see where we go from there.
There is no need to quote the whole of my post in your reply, please only quote any part you wish to highlight to me.
However please do answer this question
The other point that comes to my mind is - you say it is second hand - did it ever work Ok or were you unfortunate enough to buy it and find this problem immediately