From what you have explained the dew point temperature in the basement is lower than the surface temperature of your duct causing condensate to collect on the cold duct surface unless you have a condensate drain problem that is somehow spilling over into the duct.
First thing I would do is check the duct for rust (even galv duct will rust where it has been cut, replace the duct if you have to) then I would check for air leaks (all joints and lockseams) and seal them with a approved mastic (see IMC). To save yourself some grief, I would make sure you have at least 3 to 4, 3/8"self tapping hex head screws around the circumference at each joint (use a drill to install). You can insulate it with a foil type vapor barrier backed insulation. (I would use 2" thick insulation but that is your call) The way we used to install it was to wrap the duct with the insulation (even between the hangers and duct), staple the seams and joints with staples (with the use of a staple gun made for insulation), then apply mastic to all the joints. (We used to use foil back tape for joints but even when you apply heat or rub them with a piece of cardboard till the tape gets warm the joints always seem to come apart sooner or later.)
hope this helps
Dave