We really need more info to properly help you diagnose the problem. I am an HVAC tech and Ill be happy to help wwalk you through any checks I feel your competent to make. However, Take some of the info in this thread with a grain of salt as there was some good info presented, and very hig misconceptions thrown out as well. Feel free to PM me a numbeer and Ill contact you if you like. Having and knowing how to read a DVOM will help tremendously.
I would never Assume a Leak from no Cooling....Not as a First step for Troubleshooting. IMO its more likely he has fired up the system for the first time of the season, the compressor has sat all winter, the capacitor that starts the unit was weak and the load from a tight cold compressor did it in upon startup. The Fan on the outdoor unit would have ran as normal making it look like normal operation and the indoor unit would have ran as normal as well. HOWEVER.....this wouldnt cause it to stay on. Depending on whats staying on when the stat is switched to off completely will determine the next step in the check out procedure.
I disagree on the "TUNE UP" thoery......I dont call a coil cleaning and new filters a "TUNE UP" lik these damn companies sucker you into. Sure they say they will "Cheeck" your freon level....But in reality, if it is working properly, not only is it not needed , hooking up gauges unnecccesarily causes refrigerent loss each time, there is no way around it.
You sir sound too like you have had a capacitor fail. Its very common this time of year and I ccould make thousands on the side from spring trouble shooting and cap replacements. Typically a Regular company will charge you about $150 and up to do a simple job like this. Kills me how much big companies have to rape guys...and yes I work for one and hate the pricing. If your compressor isnt runninng, and ust the indoor and outdoor fan, it will run forever as it will never reach your desired setpoint on the Tstat and satisfy the condition.
Anyone that ever needs HVAC Tips of Help, hit me up, Im happy to help with what I feel your comprehension and skillset level is. Unfortunately Im in Dayton, so anything further than heloing on the phone is likely out of the question unless I happen to be in CBus visiting family.