After uninstalling the game again, I went to check through to see if any folders were left untouched, and there was quite a few that were not deleted/uninstalled. I completely deleted my factorio folder then downloaded the game yet again, and now I am able to join servers. Any clue why steam wasn't ...

I have uninstalled the game, deleted all files, and reinstalled it 3 times now, I've never actually touched any mods in my entire history of playing factorio

0.018 System info: [CPU: Intel(R) Core(TM) i5-3570K CPU @ 3.40GHz, 4 cores, RAM: 16344MB]
0.019 Display options: [FullScreen: 1] [VSync: 0] [UIScale: 100%] [MultiSampling: OFF] [Screen: 255]
0.020 Available display adapters: 2
0.020 [0]: \\.\DISPLAY1 - NVIDIA GeForce GTX 660 Ti {0x05, [0,0 ...

Did you or your friend change something in the game files itself? I did it myself once and got the same problem
My friend and I both reinstalled our games last night.

could you and your friend provide a log?
https://wiki.factorio.com/index.php?title=Log_File

At what point in the log file ...

My friend and I have played plenty of times in the past, as well as when it first launched on steam. I took a bit of a break from the game and decided to go back to it tonight with the same friend. Whenever I would try to join any server, I would be greeted with either "Couldn't establish network ...