When instaling Delphi 7 under Windows Vista or newer you should always use compatibility mode (Windows XP compatibility mode). If that won't work try combination of compatibility mode with administrative rights.
Also do note that you will probably need to run Delphi 7 in compatibility mode all the time.

On the other hand you might wanna switch to using FPC/Lazarus instead of Delphi 7. Lazarus use quite similar interface to Delphi 7 so you probably won't have much trouble geting used to it. Lazarus also support all the newest features present in pascal (64 bit applications, multiplatform support, etc.) and is fully compatible with newer operating systems.