We have an employee that reflows surface mount chips on Game systems. That takes a special touch. Sometimes when I need an extra capacitor from a motherboard I use the Wagner heat gun from Lowes to get it off. You can set it on the 1000 degree setting and just heat the backside for about 30 seconds to a minute. At that point you can normally tap the cap with a screw driver and it falls right out. It can cause surface mount chips to fall off if you are not careful. Wrapping with a heat shield such as aluminum foil can help. Just leave the area to heat exposed. Most boards can take the heat no problem but if you don't use common sense you can discolor the PCB a little. It will still work but it is visually unappealing.
Something like this on Ebay gets the job done.
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LoginHaving the right soldering iron has made it so we can work 10 times faster. They heat up in 30 seconds and the tips are way more precision.
I would imagine your not working boards could be easily fixed. I have repaired PCBs with fire damage. They were literally blackened. You can just follow the damaged trace till you find another solder point and attach a small piece of wire.
Good luck.