From my point of view, it is strange for the game to run in modern hardware and not able to start in a much older configuration. Usually, old games have problem on newer machines, because of different hardware parts.
The problem is the combination of a newish OS like Windows 7 on a computer with old XP-era parts that have limited driver support on Windows 7.
NVIDIA Geforce FX5500
These look like the specs a computer with XP from around 2003 might have had.
Here are the minimum system requirements for Hitchcock:
Pentium 333 mhz
128 mb RAM
32 mb video card
SoundBlaster certified 16-bits-stereo sound card
Both your Windows 7 and your Windows 10 computer are way overpowered for this game, the difference being that the Windows 10 computer has appropriate drivers for its video card while the Windows 7 computer is using Vista drivers that were tweaked to force them to install.
If you want to play Hitchcock on the P4 you might consider playing it in a Virtual Machine -- VirtualPC or VMware with an earlier version of Windows installed inside the VM.