Your computer appears to be missing some C++ and .NET dependencies that are needed to run the mod based on this (quoted) script error. Even if you have these already (as it says "TRUE" in the diagnostics that you do have them), try reinstalling Microsoft .NET Framework 4.0 and Microsoft Visual C++ 2010. Some people had this same error, and reinstalling these components did the trick and got the mod working. Don't know if it's the same case for you, but it's worth a shot.
Hope this helps you! If not, try not to load a saved game at all; instead, try to start a new game and see if you can use LCPD:FR. If you still have problems, see if you can still play GTA IV itself without any mods. Then, report back with any additional problems, error codes, etc.