I've recently purchased a Raspberry Pi 3, and after gathering all the components required, I've started to set it up. I used NOOBS to install Raspbian, and it worked fine-- that is, until I tried to connect to the Internet. When I selected my Wi-Fi router, which did show up under the Wi-Fi selection list, it attempted to connect, but would never finish connecting, nor would it show an error. I tried using many tutorials for fixing Wi-Fi on Raspberry Pi online, to no avail. I decided to get an Ethernet cable to try a wired connection, thinking that it could have been a problem using wireless. When I attached the cable, same problem. I thought I may have messed something up during the installation, so I reformatted my microSD, installed NOOBS again, and tried to connect to the Internet from there. I still had my Ethernet cable plugged in, and once again, it kept showing the "Connecting..." screen but never connected. Here is what it looked like: I waited an hour, and no change. It still just showed the "Connecting" screen.
For info, I have a WESTELL router with Frontier Internet and WEP 64-Bit security (and before you say anything about that last one, it's because my grandfather is stubborn and refuses to change it).