Dan - AC can't be tested if the outside temps are under 60 (or 65) degrees, or it could cause damage to the compressor.
Lady - I understand your concerns and desire to have these issues addressed.
Just so you know, most home inspectors use common verbiage that says systems are "beyond their life expectancy" if something is older - even if it seems to be in fine working order. They will rarely list anything as satisfactory if it is aged.
Now....to sum up....
Broken window seals are unsightly, but still structurally sound. I highly doubt the seller will give you an allowance towards that - although, they should have listed the windows to be sold "as is" - those broken seals are clearly visible, and I assume they are displaying a cloudy or foggy appearance..
It would be good to have a heating expert assess the furnace. This will give you a firmer position to negotiate. The AC is a difficult issue, since it can't be tested...not sure what the" visible signs of damage" are, but, here too, you can more than likely ask the heating expert for an opinion, as they often handle AC, too.
The wood rot incvolves some carpentry work - not sure of the extent of the damage (you might get a credit towards repair there)......imo, you probably have a slim chance of them correcting the way the patio settled, or the sidewalk.
Now, obviously, you have an agent to guide you...and hopefully you will resolve these issues with the offer of some credit issued by the sellers.
If all else fails, Jeanne's suggestion was a good one.
Look into a Home Warranty policy.
American Home Shield is a large national company. They offer some flexible plans, and should run around $500 a year - perhaps you can get the seller to take the policy out for you. It won't cover wood rot, but it will cover a functioning AC and furnace. If certain, covered items, can't be repaired, they are replaced, depending on the policy. I am sure you agent will have information regarding the warranty company her office recommends.
Best wishes to you.............I certainly hope all of this works out !
Prudential NJ Properties