What .NET framework version are you running? Are you using the free visual C# express or visual studio (even though this shouldn't really make a difference).

I think maybe the problem is not that 'DLLImport' can't find 'acknex.dll' but it can't find another dll that acknex.dll is dependant upon.

You can use a program called 'dependency walker' to check which dlls acknex.dll needs. You may also have to change your PATH environment variables.

But if normal lite-c apps work when published, then I would try re-installing .NET or updating to the newest version, if possible.