Here's the service manual for reference:
I replaced C109 with a 100uF electrolytic temporarily, and also found that the power and ground planes were shorted together. Common mode choke L10-L12 had apparently burned and shorted, so I've temporarily replaced it with jumpers.
The +7 and +5 rails are up and running now, but the 3.3 volt rail is still down. I measure about 8.6 volts from positive to negative across C109, but I'm also seeing about 8.7 volts from the ground terminal of C109 to the ground fin of regulator IC7.