The supported os for Teamcenter 10 are Win 7 SP1 x64 Pro & Ent. Do you have Pro? I do not know if the problem has something to do with the supported os but I would not recommend to install on unsupported os anyway. xtof
According to Google, your error is common on Windows when the Microsoft Visual C++ Redistributables are wrong, .NET Framework is not supported or DirectX needs reinstalled. I know people that have had trouble with the .NET Framework version and the solution was to uninstall .NET 4.5 then install .NET 3.5 and .NET 4.5 over top. The .NET Framework installation is order specific. In other words, your problems not with Teamcenter (just a symptom).