There are several related sourceforge projects that provide a COM port redirector to another com port and/or to a TCP socket. I think com0com was the virtual null modem project and that will link you to the other projects. You could also use a serial port application to do this for you - I seem to remember seeing options for that sort of thing in RealTerm and PuTTY, although I haven't used those features. Of course, how this would work depends completely on what OS your computer is running, but for Windows I think it ought to be quite straight forward.
However, the more sensible approach IMO is to put the web server on the PC, and have it communicate over the Arduino's serial port to exchange command and status messages. That will be easier to get working, quicker to develop and give you a much better solution at the end of the day.