I opened a new file to work on an animation that is only a few seconds long. I imported my audio (which is a .wav file) and pressed play, but it would not play properly - it kept glitching, turning off and on, repeating, etc. or it just wouldn't play at all (keep in mind, this is all before I even drew anything or started working on the animation). I tried closing ALL the other apps on my computer and still no luck. This is extremely frustrating. What can I do to fix it?

This has been a problem for some time: https://bugs.kde.org/show_bug.cgi?id=385589

Does the playback improve if you have an animation present? If you have an animation, does the audio render out properly into the .mp4 video output file?
My experience is that the audio does render out properly even though in-krita playback is broken.

In-program, no, the audio still doesn't fix itself when I've started animating. You're right, however, that once I render it as a .mp4 it works perfectly. It's just annoying since I need to be able to tell how well my audio syncs with the animation while I'm working on it.

One thing you could do, to give yourself a small amount of assistance as you're animating, is to have the audio file open in Audacity (or similar application) so you could select and play parts of the audio and zoom in on its timeline to see where those parts of the audio start and end. That would also help with initial overall planning of the animation.