I would probably withhold judgement on what the Radio Shack guy says. As you say, blind, and they're not known for technical expertise (which doesn't say he's wrong).
With the power in at the top right hand corner, you'll find that the circuit goes like this:
The mains fuse is near the 120V input, and then the path goes to the right, passing through a mains filter that keeps spikes out and noise in.
Next you go to the relays (and I'll talk about those more later)
Then to the smaller silver heatsink (which has a rectifier on it) and then to one or possibly both of the 200V 100uF capacitors. You would expect to find around 170V across them.
It is possible that the combined 340V (at the very least 170V) makes its way to the device on the larger silver heatsink neat the middle of the board. This drives high frequency AC to the transformer which straddles the white line (T9501).
One or more outputs of the transformer are rectified by the diodes attached to the small silver heatsink at the lower left corner and the larger black heatsink on the lower right.
I suspect the lower left produces 2 supply rails, and I suspect that the three small black cylinders (with black tops) are fuses. I would check all three of these for continuity (the board will probably label them Fxxx). If this is not the problem, then checking the diodes would be my next task.
In addition to all of this, I suspect that the components just above the middle of the board on the right are the standby power supply. See if you can trace where the output of this goes and check to see if you get an output voltage here.
The relays are almost certainly used to turn on the main power supply. I suspect that the power to (at least initially) turn them on comes from the standby power supply.
With this board disconnected, it is quite possible that the standby power supply has no way to enable the main power supply.
The relays may be a little sick. However you should see or hear something if they are trying to operate.
The photos are still not sharp enough for me to read, and you'll need to take them without a flash, it makes things even harder to read.
I suspect there's quite a few components on the underside of the board. It may be worth while looking carefully to make sure there's no burn marks on anything.