NeasdenParade,
Welcome to the HP Forum.
It is Microsoft Windows that is providing the invitation to Upgrade to Windows 8.1. The invitation might be at the Windows Store, it may come sneaking though the Windows Updates, or one might find it on the Microsoft Website and think, "It's an update... OK, I can do an update."
Microsoft does not have any idea whether or not YOUR computer can be happy on Windows 8.1, that is, whether there are HP drivers for the computer that will keep the devices running -- for example: the bluetooth or the webcam. As far as Microsoft is concerned, if you like Windows 8, you are going to love Windows 8.1 -- so "come on in, the water is fine!".
Commentary
Computer companies other than HP have the same problem with the invitation to "Update". Companies tend to populate their computers with their own software and drivers to make those computers "personal" to the company product. This is not a problem as long as you don't yank the Operating System out from under the installed driver and software versions.
The warning from HP makes sense from the perspective that many HP computers have been certified for upgrading beyond the original Operating System specifications with which the computers were sold. Other computers have not been so tested -- the warning is not specific enough to KNOW whether or not there are replacement drivers that might work for your computer model; the warning DOES know that YOUR computer is not on the magic list of "for sure" models.
One of my own notebooks, new at the time and a very expensive and very nice notebook, missed the "upgrade to Windows 8" by three months. It never was "certified". Ah, well. We move on.
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If you are happy with what you have, then stick with it.
OR
You can test the upgrade ahead time:
Update to Windows 8.1 from Windows 8
Reminder: READ the tiny print on the bottom of the page marked by the asterisk.
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If you want to know whether there are easily obtainable 8.1 drivers for your system, you can take a quick look at similar models and at your own computer's support driver page.
You can also ask for help with specific drivers by tracking down the Hardware IDs and asking on the Forum for help finding Windows 8.1 replacements.
I found seven models in your system's category:
Compaq CQ2000 Desktop PC series
Click the KudosThumbs-Up!
It is a nice way to say “Thank You" for the help.
Although I strive to reflect HP's best practices, I do not work for HP.