Go into your LFS/data folder, and make a copy of the following folders, depending on what you want to keep...
setups (self explanitory)
spr (if you wanna keep single player replays)
mpr (as above, but multiplayer replays)
skins (again, self explanitory lol)
dds (if you have custom textures or hi res packs etc)
pic (as above, plus any custom ingame menus and some sky textures will be in there)
layout (self explanitory)
engine (engine sounds, as you would expect)
sound (all other ingame sounds, if you have installed non standard ones)
Thats about it really, although i have to say, what you are describing does sound more like a controller/wheel config problem, maybe handbrake axis is inverted the wrong way possibly??