It sounds like you're trying to run more of a thin client type of program via a browser. If the audience is limited, you could install custom browsers at each workstation. I think both Netscape and IE have an SDK that let's you tweak things with their browsers. As well, you could always grab a Mozilla codebase and compile yourself.
One other thing to try would be a Java Applet that's intercepting key strokes. This is probably a bad idea, but it's an idea none-the-less.
Finally, if the target of this product is the web audience as a whole, then explain to your customer that most people aren't going to want their keys remapped for them, even if you could do it (which you can't).
Sounds like to me you're going to be buildling a VB application.
Adam