Car shakes at ideling, completely looses power if drive above 15-20 miles. Replaced transmission fluid as mechanic said it was burned

Hi I apologize in advance if this is not proper forum to ask question. I will describe the problem just in case someone can shed some light.
I have 2002 Camry 4 cylinders and has 175,000 miles. I was driving on the freeway and suddenly I felt a jerky motion and check engine light came on. When I stopped at traffic light the car began to vibrate and driving at low speeds it got me home. Admittedly, I had put lot of hard miles on the car in past 6 months and I was lazy in getting oil changed in time. It might have been 7000 miles since oil chg. I took the car to local oil change place they did not mention anything about engine but they said my transmission oil was dark and burnt. They said I should flush and replace. I agreed and tech said he had to do second flush as oil was still dark. After second flush, he said its little bit better. I was hoping this would solve my problem but unfortunately no. After oil chg and transmission fluid flush and change, Car was still vibrating. When I drove at slow speed it was driving but as soon as I tried to accelerate the car lost power. Check engine light has been on since the incident at freeway, but now check oil light and battery sign comes on as soon as you try to give little bit of gas. Subsequently, the power steering looses power. I had to park the car and restart, as long as I drove very slowly it would drive. However, if I tried to accelerate where the rpm went from one to next level car would loose power with warning lights on, power steering loss and car would stall.
I had recently replaced fuel pump, filter and any repair which was suggested to me. Admittedly, I have not replaced timing chain or belt (not sure if it matters). I would appreciate any help and assistance any one can provide?