Hello Harkanwar,
To answer your questions as best as I can:
1. The last one I tried was "HP Color LaserJet 2800 Series PS".
2. I don't know. I had a huge problem on Jan 16th getting an "HP Photosmart Premium C410a" to work, and I still only have it working as a printer, but not as a scanner or fax machine. But other than that, this problem shows up when I try to add a printer,
which is fairly infrequently.
3. My system is not on a network domain. It's Win7x64 Ultimate, with Bitlocker enabled.
4. I am trying to install the dirver that Windows has built-in when you go to ControlPanel->HardwareandSound->DevicesandPrinters->Addaprinter->Addalocalprinter->Useanexistingport->FILE:->HP->HPColorLaserJet2800SeriesPS
If you are interested in why I want to install this printer, see:
http://forums.adobe.com/message/6086519
With respect to the methods you provided, Method 1 failed to work because I don't see the printer software this pertains to installed at ControlPanel->ProgramsandFeatures->Programs. Did I make clear that I get this problem when I am trying to install the
printer, ie run the software that will install the drier software or whatever it needs? Since this step gives me the error message, I don't think the printer software is likely to show up in this list.
With regards to Method 2, I ran the troubleshooter. I asked it to look into the "Adobe PDF Converter" printer, and the only thing the Troubleshooter found was that it was not the default printer. Making it the default did not fix the problem I had printing
to it. To be fair, the only reason I have this printer around is because it was installed a long time ago. All my attempts to install it with Acrobat X or Acrobat XI have failed, presumably because of the "core driver package" problem.
Here are two of the error messages that I receive:

and:

Thank you for looking into this. I was hoping there was some way to ensure my "core driver package" is functioning properly. The little bit that I've been able to find about this problem online talks about some magic "NTPRINT.INF" file that I was hoping
if I could find after doing the right "expand" command line on my Windows 7 install disc, I could use to ensure the registry entries and DLL's for the "core driver package" are all the way they are supposed to be.