I almost felt like this repair was some kind of insider electronics trade secret and you didn't get to know until you sacrificed two virgin solder irons. I wish I could offer more help to others here, but my basic repair skill is: turn-it-off-and-turn-it-on-turn-it-off-unplug it-turn it on.....
Heidi
Ha ha ha very funny..
In repairs most of the faults are located in let say high voltage or high power parts of a circuit such as power supplies, inverters, high power output, amplifiers etc..
the parts that usually fail first are:
1- Electrolytic capacitors specially those close to heat sinks
2- Power Transistors Bipolar or Mosfets, they usually tends to go short ( the cause sometimes are electrolytic capacitors)
3- Integrated Circuits ( located in Power supplies, and output stages)
4- Diodes, and hight/small value resistors in high power circuits.
The initial approach is always visual inspection, looking for cracks in tracks, bad solder joins, "bloated" electrolytic capacitors also any leakage underneath them.
before powering up, specially after a blown up fuse look for shorts, mainly in active components ( Diodes and transistors).
Finally safety first, always ensure that the equipment is unplugged before opening it with the right tools, "try" (nobody does) keep the working area neat and clean and of course take regular brakes.
Glad that you fixed your TV
Best regards