I got it working. I had two problems.
First, as said above, I was able to get FxCop running by merging the files from "C:\Program Files (x86)\Microsoft Fxcop 10.0" into "C:\Program Files (x86)\Microsoft Visual Studio 10.0\Team Tools\Static Analysis Tools\FxCop". This made it so FxCopCmd.exe would run.
Second, I had a number of referenced external assemblies that are loaded from the GAC. FxCopCmd would only run for a very short time and wouldn't generate any achievements. I copied all relevant assemblies into the output directory and that did it. It appears it won't load from the GAC.
However, on a side note, with these referenced assemblies... I wonder if it was in any way inspecting those... because I know I code very well and there are some achievements we got that we shouldn't have. For example, 100 fields in one class. Honestly, there is no way our code ever has over 20 or 30. That had to come from something else.