Wiring – heat pump/air conditioning wiring to thermostat

If both your central air handling fan and outdoor compressor are running and your not seeing any sort of cooling after a 10-20 minutes than I'd venture a guess and say it's time to call an AC repair service.

I'm curious what you are pushing in that makes the compressor turn on? Are you somehow bridging the main capacitor? Capacitors tend to be a common point of failure on AC units and can actually be changed fairly easily. Here is a pretty good article detailing the steps to do so.

To be honest though I'd guess that the bigger problem is the fact that you can get it running and it still isn't putting out cold air. The whole situation sounds like it's low on coolant (have you had it filled in the last few years?). AC's usually have a low coolant pressure switch that will keep the unit from running to prevent damage to the compressor when there isn't enough pressure.

Call an AC service out, many will diagnose your problem free of charge and be able to give you a much better idea of your problem. Be warned though, if your system is old and uses R-22 prices have shot up in the last year.

See below, if you jumper Yellow to White the heat strips will run in both cool and heat as Yellow is energized in both modes, what makes it a cooler or heater is the O being energized in cool mode Rheems use the B terminals to be energized in heat.