The cause of the problem is because you have made the shortcut in Windows 7 to be "not a shortcut" by removing the shortcut arrow on icons (including desktop icons) by removing IsShortcut registry key. You might not remember doing so because it could have been removed by some software you installed.
Thus, to fix the issue that application programs unable to pin to Taskbar, just re-add the IsShortcut registry key back to .lnk shortcut to reset and restore back original state.
Here's how,
1. Run Registry Editor "RegEdit". You can find it by searching programs and files.
2. Before you do any thing, backup by exporting a registration file.
3. Navigate to the following registry key:
HKEY_CLASSES_ROOT\lnkfile
If you find the correct key, you'll see the following names,
(Default)
EditFlags
FriendlyTypeName
NeverShowExt
4. Add a new string value to the registry key,
Value name: IsShortcut
Value data: .lnk
5. Exit from Registry Editor.
6. Logout and login again or restart Explorer for the change to take effect.