CompleteFTP was running on Windows XP.
The problem is that they had installed the .NET 4.0 framework on the machine, but not the full version. So .NET 4.0 DLLs were being loaded, but the System.Web DLL (which is required) wasn't present.
.NET 4.0 can be installed in two versions - the ".NET 4 Client Profile" and the ".NET 4 Full Framework". CompleteFTP needs the .NET 4 Full Framework to operate correctly (as do most server applications).
This can be resolved by installing the full framework, obtainable here from Microsoft.
This isn't an issue for .NET 4.5 and beyond as the separate versions have been discontinued - there is only one installation.