Hyundai Repair: Transmission, hyundai sonata, electronic issue


Question
I have a 2001 Hyundai Sonata and if i go usually over 35mph it will start to shake like its not getting gas and if i go to turn a corner or stop when i push on the gas my car wont go ill have the pedal totaly to the floor board and it will take forever to get up to speed but if i turn my a/c off it will go with no problem and then today when i started to go from a stop sign when it went to shift into second gear it jerk really hard like it ran into something. What do i do?  
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Followup To

Question -
I believe my transmission is going out and can you tell me some things i should look out for to be sure that it is my transmission.

Answer -
There's little way to be sure unless you have the vehicle diagnosed professionally.

I will say that if your engine runs, you can shift into drive with normal feel, the speedometer stays at zero, and the car doesn't move, you've got a transmission problem.

More seriously, I can give you a much better opinion if I know what your car is doing.  Can you describe in plain language what you feel?  What the engine does?  What the vehicle does in response?

Answer
It's possible you have more than one problem.  

The air conditioning cannot affect the transmission, so the fact that turning off the a/c makes the car run normally suggests an engine performance issue.  

The harsh jerk on shift sound like a transmission electronic issue-- often caused by a bad speed sensor.

Is your check engine lamp on?  If you're looking to figure this out and repair yourself, you should find out any codes stored in the engine and transmission computers.

If there are no codes stored, I'd recommend a professional opinion.  I don't have a good feel for everything that's going on, and I'll probably never achieve that over the internet.  If a qualified technician feels the conditions happening, he'll know what sorts of things can be causing it and which things cannot cause the issues.