We are having a sliding door placed in our family room...currently, there is just a window and a very long run of baseboard heat (Hydronic I believe, there is a boiler downstairs and water goes through all the pipes).

In my Aunt's apartment, they put the sliding door directly above the baseboard heating unit, so that basically you step up to the sliding door. That is the only thing I can think of - I can't imagine taking out the current baseboard heat would do anything to help with our heating situation!!!

Also, we would like to install central AC. The house already has ductwork, but here is the deal: the vents in several of the rooms are hidden by the radiators, so the vents will need to be moved to the floor to work. In any event, there is no furnace and blower. There is a "Plenum" whatever that is. I'm guessing we will just need a blower?

It's all so confusiong. The contractor can't really give a good estimated price for this because the HVAC people have to come out and deal with it, etc.

How did the vents wind up behind the baseboard radiators? Were they added later on?

General contractors are not knowledgeable when it comes to HVAC systems. You better off speaking directly to a qualified HVAC contractor.

It seems likely that the house had forced-air heat at some time (maybe coal-fired) and it was replaced with hydronic. What fires your boiler, natural gas, propane, fuel oil?