I would have thought it would be more complex, but I only see one or two ICs that could be responsible for the actual FM synthesis.
AFAIK, the only FM synths with an even halfway complex layout were the DX7 series, which divvied up the sound-generation responsibilities between two chips (one for envelope generators, one for the actual operators) and the requisite DACs. Past that, they pretty much made all their FM stuff as single-chip solutions (although outboard DACs were still commonly required,) which I'm sure had a lot to do with the popularity of the things in arcade boards and Japanese home computers.
As for the unit, I'd look into recapping it before you go shipping it off somewhere, since that looks to be pretty easily doable and can often be a quick fix for analog-type issues (as this sounds like.) Though on the other hand you might just try to get your money back and buy one that's actually in perfect working order.
And for the record, the PDF Mongo was trying to link is
here.