I'm not totally sure how you would go about doing this with your current setup, but...
Why not have a web server running on the laptop w/ a page full of buttons sliders, etc, etc. When the user moves them/pushes them the server gets a POST request. Right?
How about having code parse the POST request, evaluate it, then send signals through the COM port?
I don't know much about getting the VEX microcontroller to listen for data being sent to it, but I could answer questions with the server stuff.
If you want to do this with ASP.net look at
this. Also, it might be kind of fun to do with Ruby on Rails. I'm pretty sure there's a ruby gem for reading from COM ports.