I accidentally burnt out my Raspberry Pi 3 Model B's 4 USB ports, and I have a touch screen that I cannot currently use because of this. The touch screen plugs into the GPIO pins, but requires a driver for it. I'd like to use the USB sticks, SD to USB adapter and the keyboard and mouse. I'd like to get a NDS emulator on it, but that requires the USB port for a SFC to USB adapter. Sorry if I'm going on too long, but I have two questions: 1. Can I replace the USB ports on it? and 2. Can I use the last 14 GPIO pins (pins 27-40) for USB, and if so, how?
Most likely when you burnt out the USB ports, you actually fried the USB circuitry on the LAN9514 combo USB+Ethernet controller. If that is the case, then you won't be able to fix it unless you have another 9514 chip and the equipment necessary to remove and replace surface-mount electronics. (Eek!)
Regarding using GPIO pins as USB, you would need a full USB software stack with the correct drivers. Unfortunately those drivers cannot exist because the Raspberry Pi's GPIO pins are 3.3 volts, and the USB specification requires 5 volts. The amount of current supported by GPIO is also significantly smaller than needed to run USB as well.
So as much as I hate to say this, you may have to go get another Pi to solve this particular problem. I really love your way of approaching this problem by not giving up though! Keep up the creative questioning of how to potentially re-use things that are available to you (like the GPIO ports)!
Take care and good luck!