Very common for older a/c systems to develop leaks. If enough refrigerant escapes, the compressor will not come on and you will feel warm air blowing out.
Any leaks should be identified and repaired prior to recharging the system.
There are also blower motors, blend doors, switches, and many other components. It takes a few special tools and some experience to accurately troubleshoot an a/c system.
Your heater cores should not cause an issue on your a/c, but it's in the same general area as a couple of your a/c components. It's possible that something got knocked loose or unplugged.
Try to describe your symptoms if you can. Is there any air blowing out of the ducts? Which ducts? Is it warm or cold? Is it blowing strong or weak? Is a/c compressor turning? Is it clicking on and off? How often? Any oily spots on your a/c lines or components? Is your radiator and condenser clean? Are all your fuses good? Funny smells? Green dye on any lines?
Even in a system with all good parts, the charge still has to be correct, with oil, and no air or moisture.
Any one of a bunch of things could cause a problem. There's a strong argument for getting a professional diagnosis and then deciding how to fix it.
