Introduction
The START/PAUSE/RESET buttons of the Atari 5200 controller can become unresponsive due to dirty/overused connections. Opening the controller and reseating/cleaning the interfaces to these sensors can improve the button's responsiveness.
Tools
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            Take off the plate and the rubber buttons. 
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            Clean the exposed contacts. 
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            Reassemble by following the steps in reverse. 
 
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                            Conclusion
                          
                          Test the controller. If these step don't improve connectivity, take a look at the circuitry replacement guide.