The speed at which your project packages is heavily affected by your CPU and your available RAM. From looking at your DxDiag, you seem to be on the lower end up the spectrum. We tend to recommend this level of hardware where your processor is about on par but your RAM is a bit low, sitting at 6 GB. This would warrant a long packaging process but not a complete stall.
To see if we can at least get it packaging, lets see if we can try to reduce the amount of assets it’s trying to package, assuming that you’re not using all of the assets in both Starter Content and Infinity Blade: Weapons. To do this, open Edit > Project Settings > Packaging and expand the options via the little arrow at the bottom of the settings list. Look for the entry for “List of maps to include in a packaged build” and hit the + button for each map that your project has. You can then hit the “…” to browse for the maps in your content folder.
If you set these maps up, whenever you package, it should only package these maps and the content that is referenced within them, ignoring anything that isn’t being used. Please give that a try and see how that works for you.