How do I fix my phone?

My phone is not working.

Long story short, I downloaded a custom ROM on my rooted galaxy s3 TGH-T999 t-mobile phone. That worked well, and was working. The only problem was that it did not have google apps, so I went back into recovery mode (I was using twrp recovery, by the way) and flashed the gapps file.

Then, when I went to reboot the phone, I kept getting an infinite stream of error messages saying "Unfortunately, setup wizard has stopped.". Every time I closed this message, a new one popped up.

I tried many things to fix it, and in the end I did a full and complete data wipe (meaning that there are no files on either the micro-sd or internal storage but the twrp recovery program).

Now there are 3 functions the phone can perform:

1. Power on. When this happens, it just shows the samsung logo and under it the carbon ROM logo infinitely

2. Boot into recovery mode. This is probably useless, however, because there is only 1 file on the entire storage system

3. Connect to a computer with a usb cable. I can access the micro-sd and internal phone storage this way

My idea was to hook up another identical s3 and copy paste the entire system onto my computer, and the transfer it to my phone so it could have an operating system and not be a brick. Should I do this?

Welcome to the forums! You need to flash the ROM through recovery. In TWRP, there's an option to connect USB to computer and transfer the appropriate ROM you want installed. Be sure to transfer Gapps as well. Wipe the system then flash the ROM then Gapps. Reboot and see if that helps. Let us know how it goes.