How to Check if DirectX 10 and 10.1 is Properly Installed
The DirectX Diagnostic Tool (opened by typing dxdiag in the Start menu search bar and pressing enter) displays which current DirectX version you have. DirectX comes with any Windows, DirectX 10 comes standard with any Windows Vista and DirectX 10.1 comes with Service Pack 1 for Windows Vista, but DirectX Diagnostics will still display DirectX 10.
If you want to be sure DX10.1 has been installed on to your PC properly, then go to your Windows folder on the hard drive you have it installed too.
For 32 bit users, open your System32 folder.
For 64 bit users, open your SysWOW64 folder.
Located the files that are highlighted on the screenshot below.
The number in the file name denotes the version. 10_1 being 10.1.
If you have 10_1, then DX10.1 has been installed on to your system.
If it isn't there, and you have SP1 installed. Then possibly uninstalling SP1 and reinstalling could fix it.