I think we should avoid patch 188.8.131.52 if you still want to play with mods. Mods dont work within this new patch. Whatever you edit like handling.dat or any other, nothing will happen. Even if you delete the handling.dat file the game will continue. Try to delete the handling.dat file, you should see that the game still works
Its like the game is using ghostdata or something.
The only way to play this game is by using that socialclub thing, otherwise you got that FC20 whatever error. The game works, but without your beloved mods!
Or avoid playing GTA4 on the PC anyway