I was driving down the road and the car surged and the engine light came on. The car is revving very high even in neutral or park and was hard to stop. Even with both feet on the brakes the car still wanted to go forward (even in neutral).

What is the car? This sounds like it could be a throttle position sensor, (TPS). This monitors how hard you are pressing the gas pedal and if it is faulty it won't be reading the pedal movement correctly. Other symptoms are uneven idle and the acceleration isn't smooth or even.

Does the problem occur when driving or only if revving the engine while in Park? If only while in Neutral or Park, that is due to the overrev limiter to prevent you from over revving the engine in a no-load situation. If this is a problem while driving, then we'll need to know what engine your Cavalier has and if there are any other symptoms (such as a rough idle, roughness at 3500 rpms and above). Also, when is the last time the spark plugs and spark plug wires were replaced? Is the Check Engine light or Service Engine Soon light illuminated?

Assuming yours is the 2 gear stick layout this is roughly how it works.
ONLY CHANGE BETWEEN 2 AND 4 WHEEL DRIVE WHEN STOPPED, IN NEUTRAL AND WITH THE PARKING BRAKE ON!!
The smaller gear shift should be to the left of the normal gearstick.
It should be in the fully forward position. This means it is in 2 wheel drive, high ratio, for normal road driving. (Rear wheels).
Pulling the stick back ONE notch engages 4 wheel drive, high ratio. Used for snowy, icy, slippery conditions as well as light off roading. (Keep the speed under 50mph).
Pushing down and back another notch engages neutral in the transfer box. This means ALL drive is DISCONNECTED even if you use the normal gearbox.
**Try to avoid this one**!!
Pulling the stick back the last notch engages 4 wheel drive, LOW ratio. This is for the more extreme off roading conditions such as VERY steep hills. Not usually used in normal day to day driving.
The two fully forward positions, (2High and 4High), will be the ones used the most.

Go to autozone or similar and have scanned for codes. You have a transmission problem.

Have the engine checked for vacuum leaks, that will cause a high idle speed. As a 35 year veteran of auto repair I can tell you that engine flushs are a 100% waste of your hard earned money.

Hello there,

This is a normal operation, all your doing is hitting the rev limiter. It's there to protect the engine from over revving. The Powertrain Control Module or PCM cuts fuel to the engine intermittently to keep the engine from revving past a predetermined RPM when in "neutral", and in "park" if it's an automatic. Just in case something like a foreign object or a small child or animal were to inadvertently depress the accelerator pedal and rev the engine too high and damage the engine in result. I hope this info helps, and just for peace of mind, I am a Master Certified Ford Technician. Enjoy your new exhaust!! I'm sure it sounds great!!

You are hitting the rev limiter top range, which cuts off your ignition.

I have a 2001 Grand Cherokee and the problem drives me crazy, but it is the way the car is designed- as soon as you hit the rev limit, it shuts down ignition and your jeep will "buck" - a real pain when you are trying to accelerate into traffic!

You have the 4.0L straight six engine, yes?

If so, please take my advice and learn to live with the minor annoyance of the rev limiter- that engine is IMHO the best Chrysler ever made (nearly "bulletproof"!) and it was so reliable you cannot even get it in a jeep now! For decades, that engine was used in welders, tractors, generators...and yes, jeeps... and it is a favorite among mechanics for its durability!

you need to clear the codes in the computer some times taking off the positive will help other times you have to bring it to a garage to clear codes

check your IDLER

the idle air control solenoid or a vacuum leak on backside of intake the hose that goes to pcv valve.they are both common problems on this car.check for vacuum leak firstthanks for your question....