You don't have to replace the whole audio amp, PC Engine boards are very repairable. In fact, if you have the original black PC Engine Duo, then your replacement audio amp would have to support both the AV port and the headphone jack, it's just not worth it.
As Abelardo said, look for corroded traces and vias. A via is a little hole where the trace transitions from PCB Side A to Side B. When I fixed the no sound problem on my PC Engine Duo (cap kit didn't restore it), one method I used for finding corroded vias was to hold the board in front of a strong light and see if any vias didn't let any light pass through. That usually means there is corrosion dust built up in the via. The easiest fix is to find the next nearest part of the overall trace and jumper over the corroded via.
Please see my PC Engine Duo repair thread before you go and waste a massive amount of time rebuilding an audio amp needlessly.
http://www.pcenginefx.com/forums/index.php?topic=21529.0In case you're wondering, the corrosion in my PC Engine Duo knocked out both the AV port audio and both left and right channels at the headphone jack.