How can I solve LionChief Santa Fe FT diesel sound problem

I'd check the obvious, try a different speaker first.

I didn't have a similarly sized speaker to try.  It is an 8 ohm 0.5 watt 2 inch diameter speaker.  I did test it with a waveform generator (I'm an electronics type person) with a 6 volt P-P 1 kHz sine wave which would be just a little above the speaker's power rating.  It sounded reasonably good.  This should be a pretty reliable test.  The sound was certainly not whisper faint.  But it is my sense that during operating I've heard it louder.  But for all I know, Lionel's circuit exceeds the speaker specification and they overdrove it a little.  I just didn't want to do that and wreck the speaker.  Maybe I'll get another speaker from someplace as a double check.  But it's my sense the speaker is OK and the problem is an electronics failure.  Such as a shorted driver transistor that is unfortunately not a discrete transistor.  They have one of those low budget assembly schemes where at least one non-packaged integrated circuit chip is directly on the board and covered with a drop of epoxy.  (That's what you'll find inside those cheap $7 Cen-Tech multimeters from Harbor Freight, by the way.)

Incidentally, I already bought a replacement on eBay from a seller that had NINE complete LionChief SuperChief sets, all with something supposedly wrong, but no description what was wrong.  (I'm trying to fix this first one to then be a fully functioning backup.)  The price was $200 for the set with free shipping which was worth the gamble.  I could find nothing wrong with the engine or anything and it is now running on the museum layout.  The passenger cars and track had never been unwrapped.  The museum layout is too small to use more cars as it already has a 5-car train.  But I just recently completed another children's layout for the Exploration Discovery Center in Grover Beach, CA which is much larger so they got the extra cars.