"For some reason, while audio in the Unity project is fine before I integrated Wwise, the integration keeps any audio from playing or being heard, and I do not know why. " - From how I read this, you used Unity audio components before integrating Wwise, and all you did now is integrate Wwise?
Yes upon installing Wwise, the Unity sound engine is disabled. Once integrated, you should start re-implementing your sounds with the components provided by the integration, like AkEvents, and so on. The Unity audio components won't work with Wwise.
Best advise I can give you, is to read through the Wwise 301 course. At least this chapter would get you started with your first sound.
Let me know if this helps.