Well, here's an interesting development, which when I look at it, makes sense, albeit annoyingly so. The code to generate a Google Custom Search box relies on using a form element to submit the search. The site admin added the GCS box after I turned the site over to him. Obviously, the additional nested form element inside the ASP.Net grand form caused some problems.

The fix was to locate the GCS in an IFrame and invoke it from a separate .html file. It's a bit kludgy, but it does the trick. And it's weird to me that the problem only showed up under IE and not Firefox. Not surprising, necessarily, just weird. :P

Thanks again for your help.