Is there a way to do this using Symbian web browser?

Nope. If the site refuses access to other browsers, then there is no easy way to change the user-agent to "lie" to the web server which browser it is.

And if the web site also depends on Microsoft ActiveX controls, then it'll be even harder, as they work only on IE/Windows.

However, if the site just discriminates against the S60 browser, try accessing it via Opera Mini.