What computer operating system is your Premiere Elements 12 running on? Have you updated the program from 12 to 12.1 using the project's Help Menu/Update? If not, please do so.
The basic questions are
a. Who set the project preset for this project, you manually or the project based on the first video drag to the Timeline? What was set? (See Edit Menu/Project Settings/General.)
On Audio 1, do you see a "5.1" marking near the track name Audio 1?
If you play Timeline Audio 1 content with the Audio Meter opened, do you see 2 or 6 channels in the Audio Meters. (See Window Menu/Audio Meter.)
What are the properties of this file...video compression, audio compression, frame size, frame rate, interlaced or progressive, pixel aspect ratio?
b. What device recorded this video/audio? And, what type of microphone(s) was involved in the recording?
I have generated the "basic questions" based on my following understanding (interpretation) of what you wrote as your problem.
Please let me know if I have misinterpreted what you wrote.
1. You have an .mp4 that has linked 5.1 channel audio to it.
2. You import it into Premiere Elements 12 with Add Media/Files and Folders/Project Assets.
Now here is where I need clarification. First you say
has a 5.1 soundtrack, the entire soundtrack plays just fine when checking or editing the preview
What are you doing at that point, double clicking the file thumbnail in Project Assets and playing back the file in the Preview Window that opens, but not yet dragging the file to the Timeline? If so, are you trimming the video in the Preview Windows and then dragging the trims to the Timeline?
But, then you say that
when I drag the video (edited or unedited) into a project's timeline, the only audio that plays is the background effects, music, etc. All the dialog on the main audio is gone. How can I fix this?
So, are you saying that, after your work in the Preview Window and your video is dragged from Project Assets to Timeline, the Audio 1 audio which is linked to Video 1 is missing some of its components that were recorded together by the recording device?