Is the turbo spooling and the tires spinning?
If you don't have a linelock, get one. It will keep the brakes cool during the burnout and make them able to hold more boost.
For the leave, the Best way to launch a turbo car is hold as much boost as the brakes will allow, then rapidly floor the gas, then Release the brakes.
The Rapid flooring will slightly bog the motor, while the turbo spools, so it will leave with more boost than the brakes will hold static.