ActiveX controls are self registering COM objects which reside on the client machine.
If you've accessed the control online, it is probably on your computer (%windir%\Downloaded Program Files).
If not, and the control is unsigned (and security settings disallow it), or if a run time license is required, or if the .inf file somehow interferes with installation, it will not be registered/rendered.
You may extract the .ocx from the cabinet, put it where you want to keep it, and register it yourself, or link to it through the codebase attribute (so it may copied to the system cache), but again, whether it works will depend on security settings and license dependencies (if any).
The specifics are covered in the SDK:
Internet Component Download
Licensing ActiveX Controls