it is not like I do not trust you, but I do not trust you.
I asked you the INTEGRAL copy of the first 2048 sectors in your disk, and NOT the copy of first sector and of sector (maybe) LBA32.
Your partition table is as follows:
Entry Type Boot bCyl bHead bSect eCyl eHead eSec StartSector NumSectors
#0 07 80 0 32 33 38 94 56 2048 614400
#1 07 00 38 94 57 1023 254 63 616448 940494848
#2 07 00 1023 254 63 1023 254 63 941111296 31455232
#3 0C 00 1023 254 63 1023 254 63 972566528 4204544
and though the size of the boot partition is not "normal" , that is usually 200 Mb (for the preview of Windows 7) and 100 Mb for the RTM version, in your case it is 300 Mb. , it is well possible that for whatever reason the good HP guys made it non-standard, as I have seen similar reports of 300 Mb partitions, this is similar to your situation:
The contents of "sector 32" appear as "hex garbage" (as expected BTW).
Please let's put aside the debate over BIOS vs. UEFI, as it has NOTHING connected to the issue at hand, which is about the "special" MBR CODE that allows, pressing F11 to start the recovery process.
the issue is that - depending on the period - HP may have used one or the other of several third party tools to create the "special" MBR, as discussed on the already given thread:
Such "special" MBR's are created for the specific machines/models and we have not found (yet) a way to reproduce them (and or even know which specific tool has been used as - as seen in that thread - over time several different tools were used by the HP engineers).
Now, it is well possible that a copy of the original MBR (or of just the code of it) is stored *somewhere* on the recovery partition and can be retrieved/restored from it, and it is as well possible that by initiating the recovery procedure the whole disk (including the MBR) will be restored to "factory state".
It is well possible that *somewhere* inside the "HP tools" or the "Recovery" partition there is a copy of the proprietary program that installs the "special" MBR.
What it is not clear (to me) is if you are willing to start a "recovery" from the recovery partition or not.
If yes, it should be possible, as said, to initiate it from a USB stick (or a CD/DVD) with grub4dos on it.
If you want to try doing the recovery process, post so, and I will guide you (hopefully) through starting it.
Alternatively, like in the already mentioned thread, I can try and help you install an open source bootmanager that may be able to replace the "special" MBR (but you will likely need to use F10 instead of F11 as hotkey):