I don't know what happened. But when I tried to play Buried in Time recently I got a strange thing where it is asking for the CDs even though it is the GOG version.
Also it is crashing/freezing at the Intro but when I select don't play intro it works.
It didn't do this when I first bought it from GOG. And I don't know if it is something that I did on my end that can be fixed.
If it can be fixed, please let me know.

Also with my older version installer, after it is installed and I try to play the game. I get this error: Unable to execute file. CreateProcess failed; code 740. The requested operation requires elevation.

The game app will ask you for a CD because it can't find the files it needs among the BITDATA - this is how the CD-ROM version functioned because all the data couldn't fit on one disc. You should never see this prompt from the GOG installation (which includes the files from all 3 CDs) unless some files are really missing. Also, the fact that the app launches but crashes during the playback of the intro movie, indicates that the file might be corrupt or missing. Since you appear to have a combination of missing and/or corrupt files, you may have a bad installation or moved the game program (or data) to a location where it can no longer locate the game data to run. I would recommend you try reinstalling or downloading again.

What Mr. Blackwood said, delete the install (backup the save games if you can find them), delete the download of your install (just to be safe), redownload, and then reinstall. Fortunately since the files aren't that big it shouldn't take too long.

Ok I used an older installer and installed it to the computer itself instead of the external hard drive and it worked. I don't know why it doesn't want to run from the external hard drive but it works.
The only problem now is with the new version installer is that it crashes at the end of install, and when I try to play that version of the game it ask for the Disc.

Then that confirms your new installer is corrupted and needs to be re-downloaded. If it couldn't run successfully through the end of the install process, then files will be missing and the game won't have what it needs to run properly.