The OpenOffice icon does appear in my Applications folder, but it does not on the desktop or in the dock, nor did it appear in the installer "hard drive."

It works, but I when I drag it to the dock, there's no icon.

OpenOffice 4.0.0

That often indicates an incomplete or damaged download file. Chances are the file you downloaded was incorrect on the OpenOffice server, it happens occasionally, or given your download speed a problem that occurred during the download. Downloading OpenOffice again will be painful with your download rate, but that is probably what you will have to do to "fix" the problem and there may be other hidden problems you have not found yet.

I downloaded it again and had the same problem. Any ideas?

When you downloaded Open Office, did you copy it to your Applications folder?

When you download it, you get a disk image (.dmg) file. Then you drag the Open Office icon to your Applications. From there, you can put it on your Dock.

Gave up on OpenOffice and stuck with Neo Office