You need to deploy the DLL to the same directory in which you copied the EXE.
You are having trouble with BadImageFormatException and not seeing c:\windows\system32 work because you are deploying your program on a machine that boots the 64-bit version of Windows. However, your program cannot run in 64-bit mode, you have dependency on 32-bit native code. You'll need to fix that by forcing your program to run in 32-bit mode. Right-click your EXE project, Properties, Build tab, change the Platform target setting to x86. Copying the DLL to the Windows directory is a really bad idea, but it is c:\windows\syswow64 on such a machine. Always favor local deployment, same directory as the EXE.
If you still have trouble with DllNotFoundException after this then the likely problem is that MediaInfo.dll itself has a dependency on another DLL. Which is pretty common, the DLL that stores the C runtime is a very common dependency. If you have no idea what DLL that might be then you can use SysInternals' ProcMon utility. You'll see the program searching for the DLL and not finding it.