I THINK I FOUND A FIX!!!
What I have done is gone to Malwarebytes and got their anti-spyware software and did a complete scan. After this scan I was able to connect through the ue4 launcher. There were some adware and even trojans on my computer and whatever was blocking the connection was fixed. Somebody get Malwarebytes, run an entire computer scan and then try to connect to UE4 Launcher. This process has worked for me and I am anxious to know if this is a fix to this problem.
A virus of some sort may be the cause of this entire problem.
Again, if anyone else has any luck, replying to this comment will really help.
Thanks!