I have successfully got Delphi 7 installed and working on Windows 8.1. This may not be relevant for Windows 7, but I tested a simple application as you suggest and I can trace into fine. I set the Delphi 7 application compatibility as follows:
- Windows XP (Service Pack 3) = ON
Settings as follows:
- Disable display scaling on high DPI settings = ON
- Run this program as an administrator = ON