Okay, so if you're on the same boat as me and found that none of these solutions helped you, you most likely have a problem where NuGet (or any of those packages) is failing to install from the VSIX program due it calling a method that doesn't exist on your computer (not sure what .dll it's referencing), so try this out from the following post:
Hope this helped someone out. It's really frustrating that the installer's log file doesn't help at all. I had to look at the log file specific to NuGet, and that's where I noticed the error:
The installation was unable to install the extension to all the selected products. For more information, click on the install log link at the bottom of the dialog.
Method not found: 'System.Collections.Generic.IEnumerable`1 System.Security.Cryptography.X509Certificates.X509ChainStatus Microsoft.VisualStudio.ExtensionManager.IInstallableExtension.get_InvalidCertificateInformation()'.