Huh? Did you probably forget to tick "No loud sample preview" in the settings?

The "No loud sample preview" option didn't help. That affects the instrument and sample editors only. It does not affect the pattern editor. I tested the behavior with an instrument and it doesn't happen with instruments. It happens only with songs containing only samples and in the pattern editor only. It does not happen within the sample editor.

All samples play at the intended volume in the pattern editor; can you please provide a small and simple example with which the problem can be reproduced? Just in case, please also provide your mptrack.ini.

It is not simply that the volume is softened. The sample is actually not playing fully. The VU-meters appear and a portion of the sound is heard, but it stops immediately on key up and the VU-meters disappear. Fade on key up is unchecked. But, it doesn't simply fade anyway — it stops.
https://skydrive.live.com/#cid=00BD6492FE45944E&id=BD6492FE45944E%21256
In there, you will find a file called Danger Room.it and the ModPlug Tracker configuration file. I recommend using sample 14 to do the sound test (as it has a loop point).

I appear to require a login to download those files.

Hmmm
Perhaps that is because they are in the public folder.
https://skydrive.live.com/#cid=00BD6492FE45944E&id=BD6492FE45944E%21116
Try that

There's no Danger Room.it, only Danger Room.wav

Oh, oops
I forgot that I uploaded it to test it with my new phone. Sorry about that
I uploaded it now (Danger Room.it).

There's nothing wrong, even with your mptrack.ini copied over - the sample plays at normal volume, and so do all other samples. No distortion happening or anything.

When you release the key, the sample doesn't stop? You are using version 1.22.03 I suspect. If it is not happening, the all that I can think of to describe it is odd.

When you release the key, the sample doesn't stop?

You are using version 1.22.03 I suspect

I am not sure how else to help try to explain the behavior. Perhaps it is an expected behavior then. Although, if it is to be expected, why does it happen only with songs that do not contain any data in the Instruments tab?

Samples have no fade-out value, nor do they have a note-off property like instruments. Hence, the only way to make them stop those endless samples at some point is to cut them on key-up. Instruments are faded out and their sustain loop is released on key-up, simpley because they have those two properties, while samples don't have them.

I can perfectly understand why this would be weird to you, given that you have so far not proven to have composed any real piece of music all by yourself, let alone in sample mode, so it's only natural that it would be odd to you when a sample is not played in its full length in the pattern editor. But believe me, all real composers are glad that they don't have to hear their looping samples forever while entering notes into the pattern. If you want your samples to be played in their full length, preview them in the sample editor.

Case closed.