To access the cheat menu, hit all 4 C buttons, the Z button, and the 2 shift buttons while in the setup option. Now go into it and you should see various codes, but none of them are unlocked. The following are the combinations that will unlock the codes:
Mass: Hold L shift + R shift and press C-up, C-down, C-Left, C-Right
Killer Rats: Hold L shift + R shift and press Z(4)
New York Cabs: Press R shift, L shift, Z, C-UP, C-DOWN, C-UP
Resurrect in Place: Hold Z + C-LEFT and press C-RIGHT, then hold Z + C-RIGHT and press C-LEFT
Frame Scale: Hold Z + C-DOWN and press C-UP, then hold Z + C-UP and press C-DOWN
Tire Scaling- Hold Z + C-LEFT and press C-RIGHT, then hold Z + C-RIGHT and press C-LEFT
Auto-Abort: Press C-UP (4)
Burning Wreck: Hold C-UP and press Z (4)
Gravity: Hold Z and press C-LEFT, C-UP, C-RIGHT, C-DOWN. Do this 3 times.
Car Collisions: Hold L shift + R shift and press C-LEFT, C-UP, C-RIGHT, C-DOWN. Do this 3 times, then press Z.
Cone Mines: Hold Z and press both shift buttons (4)
Car Mines: Press Z + C-UP then C-RIGHT, C-DOWN, C-LEFT (6)
Track Orientation: Hold L shift and R shift and press C-UP, C-RIGHT, C-DOWN, C-LEFT (4)
Super Speed: Hold L shift and R shift and press C-UP, C-DOWN, C-LEFT, C-RIGHT.
Inside-Out Car: Hold C-RIGHT and C-DOWN and press L shift, R shift, Z, L shift, R shift, Z
Damage: Press R shift, C-DOWN, L shift
Invincible: Press L shift, C-UP, R shift (2)
Invisible Car: Hold L shift and R shift and press C-UP, C-DOWN (5)
Invisible Track: Hold L shift and R shift and press C-DOWN, C-UP (5)
Brakes: Hold C-UP and C-RIGHT and press Z 3 times.
Super Tires: Hold L shift and R shift and press C-UP, C-RIGHT, C-DOWN, C-LEFT (2)
Suicide Mode: Hold Z and press C-DOWN, C-LEFT, C-UP, C-RIGHT (2)
Do the Dew!: -Long code- Press L shift, R shift, C-DOWN, then L shift, R shift, C-LEFT, then L shift, R shift, C-DOWN, then L shift, R shift, C-RIGHT (2) then press Z
Levitation: Hold L shift and R shift and Z and press C-UP 4 times.
Fog Color: Hold Z and press all 4 C buttons down 4 times.
Game Timer: Hold Z and C-DOWN and press C-UP, then hold Z and C-UP and press C-DOWN.
Stunts: Hold all 4 C-BUTTONS and press R shift, A,Z,L shift.
If one of these does not work, and easy resort is to randomly begin hitting all of the buttons (except B) at once to unlock it.
It's actually possible to fly out of the gaming environment in the Stunt course. You need the invincibility cheat for this to work. Go towards the HUGE green half pipe, and go around it to the right, and then make a left so you are travelling behind the huge half pipe, and keep going straight. You will pass a large blue ramp, and then there will be a red ramp to the left. You need to run into that at full speed, and hopefully, you will fly into the air, over the wall!
Collect all 4 Mountain Dew cans.
When at the car select screen press, Up,Down,Z,Left,Right,Z,Right,Left,Z + Down,Up,Z
Hold R - Z and press C-Up four times. Levitation time!