Neumaner

That really sucks, I enjoyed returning to LCPDFR regularly for the change of scenery :(

Looks like the automatic update check in the plugin Code3Callouts takes very long and causes it too freeze. In the RagePluginHook.ini file you can increase the time for PluginTimeoutThreshold (goes up to 60000) or try firewalling your game, which should abort the connection attempt immediately too.

Take out your mods folder and start the game.  Likely due to outdated .RPF files in the last version. If this doesn't fix it, try to start regular GTA V, and start singleplayer. Minimize the game once in SP, run the Ragehook.exe and maximize your GTA V. See if RAGE loads, otherwise:
 
COMMON PROBLEMS I'VE SEEN LATELY:
People Trying to Reinstall LSPDFR 0.2b and not installing the NEW 0.26 Version of Ragehook OVER it (leading to crashes due to the outdated RPH that comes with 0.2b)
People not removing their MODS folder in the GTA V directory (depending on the mods you installed, the asi could be loading an outdated .RPH when GTA V needs the updated version of it)
Incorrectly Installed Files or missing files(Check your installation readme, as well as your RPH.log for any OBVIOUS errors
Outdated .net framework or similar(When RPH first launches, this should come back pretty much ALL green check boxes!)

People have reported incompatible/outdated Plugins(Run LSPDFR without any additional plugins/downloads to see if that fixes it, if so updated your plugins or narrow it down)

Ok try this, start GTA V and go into singleplayer. Minimize the game, run the Ragepluginhook.exe, and maximize the game. Wait for it to load into your game (or crash it)
See if it posts a ragehook.log, then post it here
EDIT: Also, try removing the - kopie(2) from your GTA V folder. (I doubt this would affect anything, but maybe it is affecting RPH is some weird way from pointing to the right directory?) Also since I assume you have at least 2 copies of GTA V in your Rockstar Games directory, check the original GTA V directory and see if maybe the log posted there. Otherwise I am unsure what your problem is. You ARE using a legal and updated copy of GTA V right?

Yes but right when you run the Ragepluginhook.exe, Maximize your GTA V and wait. It will either load into your game or crash it. Then it may create a log