I am trying to install Unreal Engine from the Epic Games launcher, but when I try to install it it says queued and then initializing, but then it pops up a message saying the installation failed.
Have you tried the suggestions in this section of the troubleshooting guide?
If nothing works, follow the directions towards the bottom of that link to generate your Debug Logs. They are different than the log files you provided above. Post them here, along with your Dxdiag (system specs).
Based off of your Dxdiag I believe that the issue is your graphics card. It only supports up to Directx 10 and a Directx 11 or higher compatible card is required in order to run the editor.
Here is what we recommend:
Desktop PC with Windows 7 64-bit or a Mac with Mac OS X 10.9.2 or later
8 GB RAM
Quad-core Intel or AMD processor
DX11 compatible video card
Here is good place to compare and discuss hardware with other UE4 users.
So, being stubborn, I decided to keep hacking away at it and hope something worked. I uninstalled the launcher, reinstalled it, and then the install worked without any problems.
Now when I try to run the editor it says video drivers crashed. Obviously this probably has something to do with my graphics card, but I was wondering if there is any possibility of me being able to use Unreal.