What would cause a furnace to shut off prematurely?
Check the high limit switch.  If the furnace is allowed to continuously over heat, It's likely the high limit switch has burned out.

Make sure that the outlet vents are clean, and clear of debris.  You need good air flow both in, and out of the system. also make sure the heat exchanger is clean, so it can transfer heat properly to the passing air.  

If the thermostat has an option for Fan, switch it to Fan and make sure the fan starts.  If the fan does not turn on, you should contact a trained HVAC tech.  Capacitors can be deadly if not handled properly. You could accidentally discharge the capacitor into yourself, leading to electrocution. Or short the capacitor, leading to an exploding capacitor. In either case, it could be deadly.