It is the module juce_audio_devices. The DeviceManager is not needed. You can use the static methods MidiInput::openDevice() et al. instead. The AudioDeviceManager is for AudioDevices (surprise)
include is not needed. If you have added the module and created the project with the projucer, the line #include "../JuceLibraryCode/JuceHeader.h" in each cpp file includes all available juce classes.
So matkatmusic is right, no point in guessing without the error message.
EDIT: ok, double-checked, AudioDeviceManager provides stuff for Midi, but it should work without… sorry for the naughty comment… The AudioDeviceManager is intended to save and restore user settings like which device was selected etc afaik.
A thought that occurred to me, maybe the startMidi doesn’t like, that the constructor of the MidiInputCallback is not finished? Maybe try that after the constructor… but it is a shot in the blue…