I don't believe there is a way to do this through ASP (it would be a gross security violation if you could).
You can determine some information about the client browser, but not too much about the client system (just OS and version, I think). Same thing in client-side JavaScript.
Couldn't you can ask the users their timezone and save it in a cookie (or database) when they setup a profile?
There is probably a way to do what you describe with ActiveX controls, but this is also wrought with security issues and there is no guarantee that the users will "Accept" your control.
Hope this helps...
Jay