Need some help from the HVAC guys...

[shilala]

Andrew, replacing "the whole system" really makes no sense.
Your cooling side is the condenser (the unit outside), refrigerant piping, and the A coil (or flat coil) at the furnace. It generally sits directly on top of the unit, it's not tied in, or a part of the furnace.
Then there's simply some low voltage wiring that runs between the furnace, your thermostat and your outside unit.

Other than saving some coin as a "package deal", there's absolutely no benefit to your AC system in replacing your furnace. Zero, none, nada.
The thought of replacing your furnace shouldn't even be crossing your mind unless it's prone to failure, rusted out, very old, etc. For someone to just try to sell you a furnace in this instance is simply ridiculous. It should have never been brought up. I mean really, replace a 4 year old furnace just because? (I'm trying to make nice and it's really hard, I'm genuinely pissed at these guys trying to take advantage of you.)

There are a lot of flags concerning the two outfits you are dealing with. From replacing the capacitor (which is an inane, borderline retarded rookie move that guys do before they understand how to troubleshoot a system) to these guys trying to sell you a big job that you don't need done. Even replacing the compressor is cheaper and I doubt that was discussed?
I know you probably don't want to deal with yet another hvac company, but both of these assholes are trying to take advantage of you, loud and clear.
See if you can find an old mom and pop outfit who will treat you right. They won't have the great big ad in the Yellow pages. The guys who can afford those ads are the guys that sell people lots of stuff they don't need.

I can explain all the parts and pieces of your system and likely help you diagnose the failure over the phone, if you like. You should be educated before you make the move, regardless of how you choose. So far the hucksters are slinging at you pretty hard and fast. Maybe we can save you some money if we talk about it. I'll pm my number, brother.