Laptop will not shutdown

I tried all of your suggestions without success. I did delete all partitions during the original reinstall. I have uploaded the disk management screen shot as you requested though.

I was waiting for detailed replies to each step so we could put together what the problem might be. Each step should reveal more clues.

Does it Hibernate? If you disable Hibernate and program the Power button to Shut Down what is the difference between using the Start menu's Shut Down and pressing the Power button once?

This reveals if the button itself is bad. Then you'd cross the wires to see if it functions correctly.

Boot into BIOS setup to reset it to defaults after taking note of the SATA controller setting which must be replaced.

You could try enabling Verbose Status Messages.
It may help pinpoint where the problem is.

Enable Verbose or Highly Detailed Status Messages In Windows 7 | 8

@gregrocker An attempt to hibernate yields the same results as a normal shutdown and the screen turns off but all of the lights and the fan remain on. When the power button is programmed to shutdown the computer on press it brings these same results. I reset the BIOS to default although I could not find a SATA controller setting. It may be noteworthy that I have a HP UEFI computer with an Insyde F.13 BIOS version. I have read online that any advanced settings are locked from the user.

@bigmck No, I have seen this occasionally if I had a program running when I shutdown but the screen quickly closed and I do not usually see it.

@DavidE I enabled the Verbose Status messages like you suggested and I can see the difference, but most of the messages scroll by rather quickly and they all seem to be normal. What exactly should I be looking for in them?

One more thing I noticed as i reinstalled Windows 1 more time in the hopes that it might resolve the problem is that before the graphics driver is installed, even the screen will not turn off when I attempt to shutdown. It just freezes on "Shutting down..." Would this suggest a missing driver at all?

I was wondering/hoping if the verbose messages might show you where the shutdown process hung.
As all the messages scroll quickly, that's normal, it shows the "shutdown steps" process ok.
If you can tell me the last message you see, I'll do some testing and see what if anything I see after your last message.
Maybe it hangs before displaying the next message for you...

From what you said about the graphics driver, I wonder if that is the issue...
Look in Device Manager and see if there are any errors.
Did Windows install a graphics driver, did you install one, did Windows Update install a newer driver ... ?

What real-time security programs do you use ?
Anti-Virus, Anti-Malware, etc.

In addition please boot into BIOS setup and show us pictures of each tab's Settings.

Have you done a Clean Reinstall - Factory OEM Windows 7 on this HP yet?

Can you also put the model # of the laptop in your specs ?
You have an HP laptop that came with Win 8, does HP support Win 7 for your laptop model ?
In post #1 you stated

I went through various manufacturer's websites gathering the necessary drivers for it.

You installed Win 7 Ultimate, where did you get the W7 install media ?
Did you follow Greg's tutorial and download the official ISO and create media from that ?