Error 175: The specified store provider cannot be found in the configuration, or is not valid

I just joined a project and installed Microsoft Visual Studio Professional 2012 Version 11.0.51106.01 and Microsoft SQL Server 2008 R2 on a 64-bit machine.

Another team member is able to build the solution from his machine, but from my machine I get the following error:

Error 175: The specified store provider cannot be found in the configuration, or is not valid

In my .edmx file, all of the code between the <edmx:StorageModels></edmx:StorageModels> tags is marked for the error. The relevant snippet from the top of the file is:

 <?xml version="1.0" encoding="utf-8"?>
<edmx:Edmx Version="2.0" xmlns:edmx="http://schemas.microsoft.com/ado/2008/10/edmx">
  <!-- EF Runtime content -->
  <edmx:Runtime>
    <!-- SSDL content -->
    <edmx:StorageModels>
    <Schema Namespace="[NAME].Store" Alias="Self" Provider="System.Data.SqlClient" ProviderManifestToken="2008" xmlns:store="http://schemas.microsoft.com/ado/2007/12/edm/EntityStoreSchemaGenerator" xmlns="http://schemas.microsoft.com/ado/2009/02/edm/ssdl">

In doing research on similar posts, others have suggested checking the DbProviderFactories in the machine.config file.

C:\Windows\Microsoft.NET\Framework\v2.0.50727\CONFIG\machine.config

<system.data>
    <DbProviderFactories>
        <add name="Odbc Data Provider" invariant="System.Data.Odbc" description=".Net Framework Data Provider for Odbc" type="System.Data.Odbc.OdbcFactory, System.Data, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>
        <add name="OleDb Data Provider" invariant="System.Data.OleDb" description=".Net Framework Data Provider for OleDb" type="System.Data.OleDb.OleDbFactory, System.Data, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>
        <add name="OracleClient Data Provider" invariant="System.Data.OracleClient" description=".