I know this may be a long response but I promise you the information is very useful to you. I repair computers for a living (40 hours a week) and your not the first person to ask about memory. I'm only saying this because I have given detailed information about things like this on these forums and my post simply gets ignored. Hopefully you will read this and my time doesn't go to waste.
The higher speed isn't the issue.
Looking at
the manual of the dv7 your notebook supports up to 16GB of DDR3-1600. Here is a copy+paste for you. It is on page 12 in the PDF.
Your BIOS doesn't surprise me since most HP BIOS is crippled. I have not really come across many OEM (Original equipment manufacturer such as HP and DELL) machines that allow you to underclock/overclock. This is because if they gave you access to such settings and you kill your hardware they would have to warranty the hardware (which they don't want to do if YOU damaged the hardware).. Most warranty's only cover factory faults and I believe some OEM installs of Windows disable the use of software that enables you to overclock.
As for HP diagnosis.. Your machine could be in ****ing flames and it would still pass. Trust me on that one. We do warranty work for many machines and 70% of the time even though there is a bad hard drive or failing memory the diagnostics still pass on a lot of machines (this is also due to OEM being a bitch about warranty)..
As for your random restarts your machine is actually having a BSOD. Automatic restart on system failure is just turned on. If you download
BlueScreenView it should list the memory dumps and give a bit more information on why your machine was restarting.
If you weren't having any issues with the machine before installing the new memory it is most likely faulty RAM or it wasn't seated in the slot all the way. You can have the memory in there and the BIOS/OS will see it.. But it doesn't mean there is nothing wrong with the memory until it accesses a portion of the memory that is bad (portion as in between 1-2048MB in a single stick).
If you want, just before you send the new memory away (that is running at a faster speed which would put in a bit of a performance boost) run BlueScreenView and see what was causing the system failures. If you do that and there is minidumps - post what you get here I will further help you with that.
Next thing is make a
memtest86+ CD and put the new memory back in. Make sure you blow out the memory slots and install the sticks. Make sure you place them in firmly when installing them. Put in the Memtest86+ CD in and boot into it (like getting into the BIOS, tap F9 instead and it will bring you to the 'boot' menu) and just let the machine sit on memtest86+ till it gets two passes. If you see ANY failures (even just 1) then your new memory is bad without a doubt.
If you were still having restart issues before the new memory then you are having some sort of software issue.
Hope to hear back from you.