The problem was this:

My intermediary with the ISP doesn't know anything about ASP.NET; he had access to things I could not control; he didn't know what to do and I couldn't tell him. The blind leading the blind? Yes!

Well, I finally got the site to work in 3.5, which I compiled to, so that told me that my friend had not set things up as .NET 4.0. I created a start application site, or something like that, which I thought would direct things to the folder called "Company"; it didn't do what I thought it would, so I moved everything out of the company folder and put it into the root. Then things started to work.

The next day:
Got the intermediary with the ISP on the phone in a conference call with the ISP tech support guy. We discovered that the .NET framework was not set to 4.0, but between 2.0 and 3.5. Also, something was set to "Classic" by my friend, instead of "Integrated". I'm still not sure what that was. I recompiled to the .NET 4.0 Framework and re-deployed my web site files.

The web site started working just fine.