My 2001 Hyundai Elantra issue: The check engine light will come on randomly and the car will kick/jump and then the car takes forever to accelorate. Eventually the car check engine light will reset itself and the issue will temporarily go away but it's becoming scary to drive. The speed sensors have both been replaced and they say the transmission is fine but no one knows what is wrong with it.

Here were the symptoms for my 2001 Elantra before getting at the solution... My car would have very sluggish acceleration, strangely a little at or around 35mph, and then even worse at or around 55mph. It would chug and lunge, and if I floored it, the car would slowly climb in speed.
I've heard that you want to be careful to get these issues fixed quickly as these symptoms can be tough on the transmission in the mean time. So, the solution for my car was the MAP sensor. Some auto parts stores (autozone worked for me) will read your car's check engine light and be able to suggest a direction to start looking. That code pointed me to an exact answer on this site for the exact code that my car was throwing. I bought the new MAP sensor after some web research (these sensors aren't cheap after all) and two simple bolts and a wiring clip and the problem was solved! I have to admit that I tried to clean the old one first with electronics cleaner, but that didn't work at all. Good luck!