Central air conditioning system isn't working
If you can verify that there is power to the condensing unit (outside unit) then you have done all most homeowners can do.

The fan on your furnace (the thing in the basement) will come on any time the A/C is turned on. The outside unit has many safety and will not come on if any of those are not on. For instance, if your system has lost refrigerant over the years and the pressure drops below a certain point if will not come on.

Troubleshooting beyond getting power to the unit is probably something for a professional HVAC technician. Call a reputable one and make sure they give you an estimate of the charges before running up a bill.

Good luck!