I am a self-employed computer tech that has previously worked as tech support for Gateway and Sony computers.
If your motherboard/laptop is more than 2-3 years old, odds are that your moboard will not support USB3.
Un-soldering and soldering on a motherboard isn't just heating up the solder and pulling the USB port and soldering another one in.....especially if you're using a common soldering-iron. What will happen is that you'll over-heat components near the USB port.
This is something even I would avoid doing.
Replacing a motherboard is no walk in the park. The photo of the gutted laptop is no joke...and doesn't show the zillion tiny screws you hope you remember where they went when you're re-installing.
If you have one working USB port, go buy a USB hub that has a power-supply. They cost less than $15 for a decent one.
You may want to disable the broken USB ports in your device manager. If either are shorted out due to the breakage, you may end up having other problems.