Been very humid in KY this summer, and I've got a problem with condensation on the ductwork. House is a walkout with the basement fully finished; furnace and A/C unit is in a utility room in the basement; ducts and returns for basement and first floor runi bewtween basement ceiling and floor of first level; ceilings are drywalled with the exception of the utility room. The condensation is noticeable at the unit and on the ducts as they leave the room into the finished spaces. Insulation is an answer, but how can you do it if you have no access to the majority of the ducts?

Not a pretty thought,condensation will spot up and ruin drywall

It should have been insulated before drywall was put up

We are the first owner's to live in the home, but it was built for someone else--completed 1 1/2 years before we bought it from the bank. This hasn't been a noticeable issue in the previous ten years we've been there, and its something I would have noticed.
I've got a dehumidifier running in the utility room, but the condensation has not diminished yet. I would hate to do it, but removing the ceiling drywall to wrap the pipes seems to be the only complete answer. I'm wondering if there is any type of spray-in insulation that could be done from inside the ducts. I know there is an aerosol sealer that can be introduced into the ductwork to seal leaks, but not aware of any insulation.

Anything put on the inside would possibly cause restriction on the amount and quality of air going through the ducts,the dehumifier and maybe a second one will be a major help

Your situation is not a good one.
If you do insulate the accessible ducts and not the other it will increase the condensation in those.
Returns do not need to be insulated as they do not have enough temperature differential above the inside ambient temp to cause condensation. The dew point is the real factor.
Commercial systems do actually employ insulation on the inside of the duct system, and they are designed for that friction loss and sized accordingly, but that is not an option for you.
If you can't get to it you can't do anything to it.
One option would be to cool that space above the basement ceiling and below the floor system above so as to reduce the temperature differential and probably stop condensation.
The bottom line is any properly installed H/VAC system should have had all the supply ducts installed from the start.
It sounds like the system was converted from heat only to both heat and cool and they skipped an oh so important step!
Hope this of help to you.

Thanks Tech. It actually was not converted from heat only, it was a combo frm the start. Just a bad job from the contractor. It's been awhile since they did this job and when they did the work for the builder it was just Lot #232-did not remember doing the work. I had one of their sales guys here about doing a maintenance contract for the system. Showed him the system and he said "whoever put this in didn't do a very good job of it.". I laughed and told him that his company did the install. Needless to say he was very red faced and left quickly.
I'm working on the dehumidifiers right now to see if they can alleviate the problem. If so, great. If not, then I'm looking at cooling my floor space or ripping out drywall.

Good luck with dehumidifiers, although I do not think that will solve your problems since the space above your basement is isolated from the space below. Not sure what you mean by cooling your floor space... and ripping out drywall would not be needed either. The best most economical solution would be to see if you can equalize the temperatures in the basement and the enclosed space above the basement and the below the first floor by allowing conditioned air to cool that, and allow for return circulation of air into whatever you may have in the basement.

The utility room is about 6' x 8', and the ceiling is open and accesses the rest of the space between the basement and second floor. I put the dehumidifier in the room and it has stopped the condensation from occurring. I have talked to the original contractor again, and they "cold not understand" why the ducts weren't sealed and insulated when installed as that was their "standard procedure". They are willing to work on getting a solution for this so that's our next step.

The utility room is about 6' x 8', and the ceiling is open and accesses the rest of the space between the basement and second floor. I put the dehumidifier in the room and it has stopped the condensation from occurring. I have talked to the original contractor again, and they "cold not understand" why the ducts weren't sealed and insulated when installed as that was their "standard procedure". They are willing to work on getting a solution for this so that's our next step.