Changing the lettering on the side of the car will not fix your game.
However if you must know, you need to use sparkIV to open the texture file of the vehicle, find the layer you want to edit, export each of those layers that you want to edit as .png files, open them in an image editor like photoshop, erase the LCPD lettering and then use a text tool to rewrite NYPD, then save it as a .png, open up sparkIV, open up the texture files for the vehicle, find the layer that you have edited and import the image you just made in photoshopped to replace the old verison, then save.
Alternatively, find a dodge charger skin that someone has made, there are probably quite a few in the downloads section of this forum and then replace the textures as directed.
However, fixing your game is another story.
How many car mods do you have installed? What ones?
Do you have ELS installed and how many cars are using it?
What other ways have you modified the game since it was working correctly?
What is your resource usage as per the options tab in the game menu?
Also fyi, the problem you are having now does not seem to be related to LCPDFR so you are free to attempt to find your problem by consulting other message boards or googling your problem to see what other people have done to fix the same situation.