A resistor with current flowing through it will exhibit a voltage drop. I can't really tell what part of the circuit this resistor is in from the pictures but with 0.76V on one end... is it connected to the base of a transistor by any chance? If so, then that reading is likely perfectly normal if this resistor is in fact biasing a transistor.
Anyways, properly diagnosing such a power supply requires a good understanding of the topology and functional description of such a power supply. It's actually two power supplies in one. The +5VSB power supply, with its corresponding transformer T3, which is always active when plugged in to AC power, and the main power supply through T1. T2 provides isolation to drive the gates/bases of the main switching transistors, these switching signals would come from the main IC in the bottom right corner of the PCB (looks like possibly a TL494 or equivalent?).
When you ground out the green wire, that sends a signal to the main switch IC to be enabled and produce switching waveforms to drive the switching transistors. It also handles voltage regulation and feedback, as well as over-current protection and other protections if applicable (again, depends on what the IC is that's being used).
Since you have +5VSB, the next thing to check would be the output of the main switching IC for a switching waveform, using an oscilloscope (CAUTION: unless you have a suitable isolated probe or isolation transformer, DO NOT attempt to connect oscilloscope to any part of the primary side of the power supply under any circumstances!!!). If there is no waveform, the next task is determining why, and that will require a bit of reverse-engineering of the circuit (usually made easier by referencing datasheet for the IC and typical application diagrams).
All this being said, when you're done using this power supply as a learning experience, PLEASE put this thing where it belongs: in the bin. The thing that really stands out as far as this being a complete piece of crap is the jumpers in place of LF1 and LF2. This power supply very likely does not meet EMC regulations, at the very least.