I'm trying to install Psychonauts and Sacrifice, but the installation packages aren't working. Sacrifice package I can see running in the Task Manager as Setup_Sacrifice (albeit with the minimum 100KB) but it just sits there and the Install prompts don't show up, and it takes several minutes for Windows to close the process when I right-click and select End Process. The Psychonauts package starts to run the Integrity Check, but freezes about a quarter way through. If I Skip the check, it will begin to install, but the installation progress bar freezes a quarter way through. What's going on here?

Turn UAC off before installing . . . =)

Try keeping the install going. It could take awhile to actually initialize.

I disabled UAC when I installed Windows.

I'm sure you are right clicking and installing as an admin so . . . my next step would be to disconnect from the internet and disable my Firewall and AV and then give it a try. Make sure Windows Defender is of as well.

I thought the purpose of disabling UAC was to be able to skip the step of "Run as Admin". Webroot ISE's Execution shield has never interfered with a GoG installation package before, but I did disable it anyway just to see. Windows Defender is a bad joke, so I leave it off by default.

The Psychonauts installer did complete, but after two and a half hours. The process was marked by long periods of inactivity interspersed with sputters of active installation.

I should mention that these packages were downloaded on another computer and moved to this one via thumb drive. I paid for them, of course, just not at my house. I didn't mention it before because I didn't think just transporting the files would make any difference in their performance.

I've had problems with GOG installers when moving them with a USB key or drive. They didn't open, and failed the integrity check. You should avoid this by burning them to say a DVD, that might help with the integrity problem.
Note here that I'm still using WinXP, so it can be purely a W7 problem.

Even with UAC disabled you should run the install as an admin. Also on Vista and Win 7 I install everything in a directory outside of Program files. UAC seems especially interested in stopping certain activities in the Program Files directory. Also make sure the game shortcut Compatibility tab has "Run this program as an administrator" checked.

Not running an install as an admin OR with UAC on can cause disk writes / registry writes to be blocked.

Moving the files should not make any difference in the install. UAC is known for causing the symptoms you describe. Not running as an admin can result in a partial install due to blocked disk and registry writes.

One other thing to check that causes a similar problem . . . make sure you have enough disk space to install the game.