The solder joints are fine in your picture. I would focus in on the power supply after you have tested the outlets!
A surge or lightning strike could have damaged your power supply are you using a surge suppressor or better yet a UPS? I often find power supplies get damaged from bad outlet and building ground circuits.
Looking down on the righthand side of the logic board you should spy a strip of black tape as seen here
Reading from right to left what LED are on when you plug in the iMac and then press the power switch?
LED Functions
LED #1 - Indicates that trickle voltage from power supply has been detected by logic board. This LED will remain ON whenever the iMac is connected to a working AC power source. The LED will remain on even when computer has been shut down or put to sleep. The LED will turn off only if AC power source is disconnected or power supply is faulty.
LED #2 - Indicates that logic board has detected power from power supply when computer is turned on. This LED will be ON when computer is turned on and power supply and voltage regulators are working correctly.
LED #3 - Indicates that computer and video card are communicating. This LED will be ON when computer is communicating properly with video card. If LEDs 1 and 2 are ON and you heard the startup sound, but LED 3 is OFF, then video card might be installed incorrectly or need replacement. Note: LED #3 is not present on models with integrated graphics.
LED #4 - Indicates that computer and LCD panel are communicating. This LED will be ON when computer is turned on and video signal is being generated. If LED 4 is ON and there is no image on display, then LCD panel, LED backlight board, or cables between might be installed incorrectly or need replacement.
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To be clear you turned the system on normally from the power switch on the system and in doing so you got a power zap?
If this is the case unplug the systems power cord and all the other devices using the same outlet. Check your power outlet to make sure its wired correctly and properly grounded. Get one of these outlet testers Outlet Tester and here's more on its use A MUST HAVE TOOL - The Electrical Outlet Tester - How to use and why you should have it
If you find a problem get an electrician to fix it as well as check the breaker panels ground connection is bonded to a good earth ground point.
If the tester appears to show no problems carefully plug the peripheral devices back in and use the outlet checker on the power strip you are using to make sure one of the devices is not shorted out to ground. Then test your iMac last.
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