When my car is stopped, it shakes. Also, the car hesitates when I accelerate and I have to floor the accelerator pedal in order to speed up. When I was performing a tuneup on the spark plugs, there was some oil around the thread and there was a dark/burnt look on the tips. So I replaced the spark plugs, gasket, valve cover gasket, and seal. The shaking is slightly better, but not much, so all of that actually did not solve the problem. What is your advice for what will fix the shaking and hesitation problems?
You don’t mention the Check Engine Light being on, but if so, check trouble codes before any other diagnostic activity - usually saves time! Good call on your initial repair - oil in the spark plug well can short the spark plug, causing a "miss" from that cylinder. It’s possible you have a bad ignition coil (or more), or some other problem like a blown head gasket causing one or more cylinders to misfire. A professional mechanic, like a certified technician from YourMechanic, can check for good spark, good compression, and proper fuel injection on each cylinder to isolate the problem and make repairs.
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