I had the same problem after upgrading from XBMC to Kodi this morning. I'm running Windows 7 Home Premium, and there's nothing too out of the ordinary about my system.
Anyway, I was receiving the error message about missing the msvcr120.dll file, followed by the additional "Uh oh" error message about the file sqlite3.dll.
I did manage to get things working again by doing the following:
1.) I copied the file sqlite3.dll from the C:\Program Files (x86)\Kodi\system\ folder to the C:\Windows\SysWOW64\ folder.
2.) I downloaded and installed the Visual C++ Redistributable Packages for Visual Studio 2013 from Microsoft available here:
http://www.microsoft.com/en-us/download/...x?id=40784
Since I have a 64-bit system, I first installed the x64 version of the Visual C++ Redistributable Package, but since it occurred to me that Kodi was installed into the Program Files (x86) folder, I wasn't sure whether it would want the x86 version of the Redistributable Package instead, so I ended up installing both. It was probably overkill, but I didn't feel like messing with the problem for very long (what can I say, I'm lazy). I installed the x64 version first, then the x86 version, and then re-ran the x64 version one more time and did a "Repair" install.
After that, I tried to start Kodi again, and everything worked fine. Hope that information helps!