TDM as of 2.06 seems to require some DLLs that aren't part of Windows 7. I think it is a C runtime or something. One thing that'd be great is to put a blurb about this on the download page with the correct link to the needed files, as searching for and downloading random DLLs online is a good way to get in trouble (malware).
It requires only MSVC 2013 redistributable package.
Both 32-bit and 64-bit installers of it are automatically downloaded by tdm_updater into your directory. They are named vcredist_x86.exe and vcredist_x64.exe.
Moreover, tdm_update actually runs them silently during installation, although for some people it does not succeed. I would be glad if someone points me out why.
If you have some DLLs missing, simply run these two exe files already present in your TDM directory and make sure they succeed.
Never download separate DLLs from internet, you can get into great trouble. Aside from a chance of getting a potentially compromised DLL, you also create DLL hell which will surely bite you in future.
If you want to install the package yourself, go to Microsoft site and download MSVC 2013 redistributable package. Do not download anything from any other site except Microsoft (and TheDarkMod).
P.S. Do we have a popular installation FAQ/troubleshooting instructions? We should add an advice to run vcredist_x86.exe and vcredist_x64.exe installers in TDM directory if TDM does not start after install/update, asking for a DLL.