DllNotFoundException with CLEyeMulticam.dll after .NET target version change

I am using the CLEye framework to interface with a PS3 Eye Camera and have had it working just fine for a while now. I recently tried changing my Target Framework in the properties menu from 4.5 to 4.0 and found that doing so causes the error System.DllNotFoundException: Unable to load DLL 'CLEyeMulticam.dll': The specified module could not be found. (Exception from HRESULT: 0x8007007E) to happen whenever I attempt to call a function from that DLL. Now any framework that I select (4.0, 4.5, 4.5.1) all show the same error.

I have previous gotten this error before I installed the CLEye SDK but haven't seen in since then.

Based on other SO questions this is usually caused by the DLL having unresolved dependencies. It is hard to imagine that this is the case here as I don't think I could have changed this dependency since it had been working. Is there something related to changing my target framework that could have broken a dependency? Should changing back to my original target framework fix the issue?

via Chebli Mohamed