Visual Studio 2012 is no longer able to interact with any TFS server

Question

I can connect to the on-premise TFS2012 server using the instance of VS2012 installed on the server machine as well as the instance of VS2012 installed on a coworker's machine.
I was able to interact with TFS2012 using the instance of VS2012 installed on my Win7 x64 machine, but only one time. Many reboots later, both of the server itself and my machine, I haven't been able to get VS2012 to interact properly with TFS.
When I click on "Team" and select "Connect to Team Foundation Server", the "Team Explorer" VS window opens. In that window, no matter what button or link I click on, Visual
Studio won't connect to TFS or allow me to choose a TFS server.
1. Clicking on the Home icon takes me to page with two buttons: Pending Changes & settings.
Clicking on "Pending Changes" takes me to a page where I can do 3 things: click on "no workspace" (nothing happens), click on Actions -> Open Source Control Explorer (which opens an
empty Source Control Explorer Window, from which I can do nothing), click on "Settings", which shows me a page with 4 options:
Security: clicking it results in the message "Team Foundation Error. Object reference not set to an instance of an object"
Group Membership: clicking it results in the message "Team Foundation Error. Object reference not set to an instance of an object"
Source Control: clicking it results in the message "Value cannot be null. Parameter name: serverName"
Process Template Manager: clicking it results in the message "Value cannot be null: Parameter name: tpc"
2. Clicking on the "Connect to Team Projects" icon takes me to a page where I can click on either:
"Configure Team Projects": clicking it does nothing
"Connect": clicking it does nothing
"Sign Up": opens a Visual Studio Online page on my web browser
If I instead go to File -> Source Control -> Advanced, there is only one option which appears to be working:
Change Source Control. When I click on it I get a window with a table with rows that correspond to the current solution and the projects in the current solution. ie:
Solution/Project: {item name}
Server Name: "<No Server>"
Server Binding: "<No Server>"
Connected: {gray uncheckable checkbox}
Status: "Not Controlled"
Local Binding:
Provider:
Relative path:
The buttons "Connect", "Disconnect", "Browse" are disabled. Clicking on the "Bind" button results in a window with the message "The mappings
for the solution could not be found" and two buttons: Ok and
Help. Clicking on Help results in a white window with the message:
"The 'EurekaPackage' package did not load correctly. The problem may have been caused by a configuration change or by the installation of another extension. You can get more information by examining the file 'C:\User\<username>\AppData\Roaming\Microsoft\VisualStudio\11.0\ActivityLog.xml'.
Continue to show this error message?"
Clicking "yes" open the following page on my web browser, which essentially tells me to go back to the "Change Source Control" window and unbind the project, which VS is not letting me do:
http://msdn.microsoft.com/query/dev11.query?appId=Dev11IDEF1&l=EN-US&k=k%28vs.tfc.sourcecontrol.MessageConnectionManagerCantBind%29;k%28TargetFrameworkMoniker-.NETFramework
The following is an excerpt from the "ActivityLog.xml" file mentioned in the white window that appeared when I clicked on the "Help" button:
  <entry>
    <record>651</record>
    <time>2013/12/20 13:35:53.354</time>
    <type>Information</type>
    <source>Profile manager</source>
    <description>Begin export of category &apos;Source Control_TeamFoundation&apos; ({2A718788-A6D9-44C5-90EF-438BF5B06A74}) from package &apos;Microsoft.VisualStudio.TeamFoundation.VersionControl.HatPackage, Microsoft.VisualStudio.TeamFoundation.VersionControl, Version=11.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a&apos; ({4CA58AB2-18FA-4F8D-95D4-32DDF27D184C}).  3349472 KB of virtual memory currently available.</description>
  </entry>  <entry>
    <record>652</record>
    <time>2013/12/20 13:35:53.354</time>
    <type>Information</type>
    <source>Profile manager</source>
    <description>End export of category &apos;Source Control_TeamFoundation&apos; ({2A718788-A6D9-44C5-90EF-438BF5B06A74}).  3349472 KB of virtual memory currently available.</description>
  </entry>
  <entry> <entry>
<record>664</record>
<time>2013/12/20 13:48:51.961</time>
<type>Error</type>
<source>VisualStudio</source>
<description>CreateInstance failed for package [Microsoft.Data.Entity.Design.BootstrapPackage.BootstrapPackage, Microsoft.Data.Entity.Design.BootstrapPackage, version=11.2.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a]</description>
<guid>{7A4E8D96-5D5B-4415-9FAB-D6DCC56F47FB}</guid>
<hr>80070002</hr>
<errorinfo>Could not load file or assembly 'Microsoft.Data.Entity.Design.BootstrapPackage, Version=11.2.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a' or one of its dependencies. The system cannot find the file specified.</errorinfo>
</entry>
<entry>
<record>671</record>
<time>2013/12/20 13:50:19.757</time>
<type>Information</type>
<source>VisualStudio</source>
<description>Entering function CVsPackageInfo::HrInstantiatePackage</description>
<guid>{E8B06F41-6D01-11D2-AA7D-00C04F990343}</guid>
</entry>
<entry>
<record>672</record>
<time>2013/12/20 13:50:19.757</time>
<type>Warning</type>
<source>VisualStudio</source>
<description>Unexpected system error mode before loading package [Visual Studio Web Browser Package]</description>
<guid>{E8B06F41-6D01-11D2-AA7D-00C04F990343}</guid>
</entry>
<entry>
<record>676</record>
<time>2013/12/20 13:50:19.820</time>
<type>Information</type>
<source>VisualStudio</source>
<description>Entering function CVsPackageInfo::HrInstantiatePackage</description>
<guid>{8C28E535-ABC9-4F92-B5C9-6C16617C8884}</guid>
</entry>
<entry>
<record>677</record>
<time>2013/12/20 13:50:19.820</time>
<type>Warning</type>
<source>VisualStudio</source>
<description>Unexpected system error mode before loading package [EurekaPackage]</description>
<guid>{8C28E535-ABC9-4F92-B5C9-6C16617C8884}</guid>
</entry>
<entry>
<entry>
<record>679</record>
<time>2013/12/20 13:50:19.820</time>
<type>Error</type>
<source>VisualStudio</source>
<description>CreateInstance failed for package [EurekaPackage]</description>
<guid>{8C28E535-ABC9-4F92-B5C9-6C16617C8884}</guid>
<hr>80070002</hr>
<errorinfo>Could not load file or assembly 'file:///C:\Program Files (x86)\Microsoft Visual Studio 11.0\Common7\IDE\Extensions\Microsoft\Web Tools\Eureka\Microsoft.VisualStudio.Web.Eureka.dll' or one of its dependencies. The system cannot find the file specified.</errorinfo>
</entry>
  <entry>
    <record>559</record>
    <time>2013/12/20 14:30:48.880</time>
    <type>Error</type>
    <source>VisualStudio</source>
    <description>Could not convert file time to system time</description>
    <hr>80070057 - E_INVALIDARG</hr>
  </entry>
</activity>
What, if anything, can I do in order to be able to get Visual Studio 2012 to interact with TFS?

Answer 1

I'll add that when I run devenv.exe with the flag /TFSLink, VS opens a Team Explorer window that contains the following text:
An exception was encountered while constructing the content of this frame. This information is also logged in "C:\Users\<username>\AppData\Roaming\Microsoft\VisualStudio\11.0\ActivityLog.xml".Exception details:System.NullReferenceException: Object reference not set to an instance of an object.   at Microsoft.VisualStudio.Shell.Interop.IVsShell5.LoadPackageWithContext(Guid& packageGuid, Int32 reason, Guid& context)   at Microsoft.VisualStudio.Platform.WindowManagement.WindowFrame.GetPackage()   at Microsoft.VisualStudio.Platform.WindowManagement.WindowFrame.ConstructContent()