Have you tried running them in compatibility mode with "Visual themes," "Desktop composition," and "Display scaling on high DPI settings" disabled?
Also try both XP and 2000 compatibility, and even 98 compatibility for the oldest games.***picture of options on compatibility tab***
Have you tried installing them to your user's Documents folder instead of the default location? Windows blocks some games from installing to or running from C:\Program Files and C:\Program Files(x86).
Have you tried both installing and running them as an Administrator (using the option in the right-click menu)?
Have you confirmed that the problem isn't a widescreen monitor problem rather than a Windows 7 problem? Some games will start if you change your desktop resolution to what the game uses instead of starting from your usual desktop resolution. Even if you don't have a widescreen, sometimes starting a game from a lower resolution than normal on an LCD monitor will help the game start.
In Memoriam may not run because of a QuickTime problem or because the website that's necessary to start the game has moved.
The Egyptian Prophecy is listed as one that won't run in Draclvr's thread, but the Nancy Drew game should run. Maybe the problem with the Nancy Drew is similar to the problem listed for Stay Tuned and Royal Tower (that's a guess though). The Egyptian Prophecy might run inside VMware Player or Virtual PC, but I haven't confirmed that.
Draclvr's thread has a fix for Scratches:
Scratches installed, but trying to play the game caused a BSOD and a memory dump. Upsydaisy reported the same result on her newly installed Windows 7. I tried playing both from a full installation and playing from the disk - same result.
EDIT for Scratches. Inland and I found a work-around posted by the game developer. You must edit the Scream.CFG file. To accomplish this in Windows 7, go to C:/Program Files/Nucleosys/Scratches. Find the Scream.CFG file and right click. Select Properties and from within that window, change the Open With option to either Notepad or Word Pad. Change the Rate from 0 to 60. Save the file, exit and restart the game.
Draclvr and Inland are the real experts here, and other Gameboomers members have a lot more first-hand experience than I have. I've used Win7 for office stuff, but not games.