Thanks to the hard work of D-Lite (http://nfggames.com/forum2/index.php?action=profile;u=167), I followed his quick n easy guide (http://www.pcenginefx.com/forums/index.php?topic=702.0) to replace the single component that cripples the sound on the Turbo Express. In a nutshell, one single capacitor neutralizes the audio amp, so the speaker is basically silent unless you hold the machine against your ear.
There's nothing to it: Open your system (six screws) and solder a new 100uF capacitor to two ready-to-use points. I used a 16V capacitor 'cause it was available, but anything over 6V will work.
(http://gamesx.com/grafx/TE-repair2-1.jpg)
(http://gamesx.com/grafx/TE-repair2-2.jpg)
That's all there is to it. Instant volume fix!
The capacitor is placed where it won't interfere with anything. I routed the wires around the brown connector to hold the capacitor in place.