Schizm is Mysterious Journey....right? I have and played Mysterious Journey II on Windows 7, but I think Mysterious Journey I might be too old,
If Mysterious Journey 2 works on your computer, Sentinel probably will too. Sentinel is made by the same company as Mysterious Journey 2 and uses the same game engine. The first Schizm uses a completely different game engine and you might have problems with it on a new computer. When I played it in Windows 2000 it had audio problems.
I had Shivers I & II, and loved them, but neither would play in windows 7. I tried Shivers in the Virtual XP mode, and it half played but screen was very small and it jumped all over the place.
I'm not too surprised that Shivers wouldn't work in XP Mode. Shivers was made for Windows 3.1/95/98 and XP Mode is meant for programs that were made for XP. The small screen size was due to the fact that Shivers runs in 640x480 resolution and unlike later games, does not automatically change your screen resolution when you start the game. You'd have to reduce your desktop resolution to make Shivers appear larger on the screen.
Many older games, including Shivers and any game that uses an old version of QuickTime, work great in Virtual PC. Since there are so few of these Myst/Riven-like games, it might be worth your while to set up Virtual PC on your computer. You'd need a Windows 98 install disc to install Windows 98 on the Virtual machine. There are instructions
***here***.