We'll assume that you haven't swapped the fuses...that the 5A fuse and the .1A fuse are both in their proper place.
The circuit that the small fuse supplies simply triggers the main power relay. This consists of the small transformer, a diode bridge, two 100µf caps, and the power relay with it's associated kickback diode. I'd desolder the bridge and do a diode check on it, as the most likely failure is the diode bridge or the kickback diode. A plain 1N4004 will work for the kickback diode (Dz1) and although I can't check on the pin spacing, it looks like Digikey #KBP02G-ND might fit OK for the bridge (Dz6). The Digikey part has a pin spacing of about 3.75mm.
And yeah, I'd replace the electrolytic caps on that board as well.