I have Trend Micro anti-virus software and I think that caused this error for me. I turned Trend off and switched to the European server without hitting install, then back to the NA server and now it's installing just fine.
The error message "webget request failed" can be caused by a variety of reasons. Below are several possible solutions to the problem.
•First, try starting the program through the Start Menu.
•Click Start.
•Then All Programs, then The Elder Scrolls Online Beta.
•Instead of left clicking on an item as you generally would, players should try to right click on it and to select Run as Administrator.
If this does not help, players should try to temporarily disable their virus protection, firewall and ad blockers in their browser. Most virus protection programs have an option to be temporarily disabled by right-clicking on their icon in the lower right hand corner and selecting the "Disable" or "Suspend" option. Once the game has been updated, please remember to turn them back on.
If players are using Trend Micro security software, they should be aware that it will block ESO even when disabled. They will need to add ESO as an exception. To do so:
•Open the Trend Web Threats in the main console
•Click on Threats Stopped
•Click on Web Threats
•Players will see it is blocking www.elderscrollsonline.com
•Click on this and approve the site
•Open the launcher
If neither of the above helps, players should try to update during off-peak hours. During peak times, the general congestion on the internet can cause information to not be delivered correctly, resulting in this error.
Addendum: The previous fix didn't pan out but I found the solution in the knowledge base as follows
To do so:
Open the Trend Web Threats in the main console
Click on Threats Stopped
Click on Web Threats
Players will see it is blocking www.elderscrollsonline.com
Click on this and approve the site
Open the launcher
I had this problem and just managed to get round it. It was to do with my internet provider and my router. I am with Virgin Media, apparently their new firmware update clashes with the ESO update launcher and so you end up with the "web get request failed".... I had it for ages...
Long story short. Turn your router to modem mode and it should work. Mine did and I have been happily playing it since. I hope this at least works for some of you!! If not then I hope they can help you get round it.