The technician came out yesterday and determined that there was a bad 4-ton evaporator coil and a few other parts.I received a notice from AHS saying that only some parts would be covered.

Hot water is also provided by the boiler (via a tankless coil inside boiler). 

@Peter Morgan Residential HVAC systems have two components (hence "split"): an indoor unit (evaporator coil) and an outdoor unit (condenser coil).

I had a service call last year for AC not working and it turned out it was a plugged HVAC filter that lead to the coil freezing.

Like was already asked, is there a scuttle large enough to get a furnace and evaporator coil through?

I have been told that my air conditioner "The system unit needs to have Freon up to 8lbs to 9lbs and replace Coil Condenser.

for Air Conditioning parts like an evaporator coil, or a condenser? 

I have an issue with an A-coil it took a little over a year for the Freon to empty out. it was determined that their is a pinhole. 

I would upgrade, for many reasons. 1, there's no guarantee that the replacement refrigerants won't keep going up in price. 2, it's an old unit so eventually you'll need a new compressor, coil, or other major component.

One guest group closed air vents, so the coil was frozen ....