My tenant is moving out and couple of relatively major issues have been noted. 1) lot of condensation on one window which the tenant has never disclosed.

They also sometimes have issues with condensate build-up, which can lead to water leaking from the unit.

Yes, the A/C condenser, coil, and furnace will replaced; those will be done by a separate HVAC company.

@David FernandezTechnically your boiler is an HVAC system (heating), but I gather you are contemplating replacing the hydronic heat with forced air.If the property is in an environment where there is a significant cooling season, then the extra cost of switching to a central air handler (i.e. heat pump w/ ancillary gas for additional heat), removing the radiators and lines and installing ductwork may make longterm sense.If there is not a significant cooling season, then it would be far more economical to replace your old boiler with a new high-efficiency condensing gas boiler (~95% efficient).  

Furnaces, Boilers, Steam Boilers(What you use), Condensing Boilers, Heat Pumps, and Electric Baseboard.

That will stain over time when wet or from heat and condensation, but that doesn't look like paper the way it flows down.Black tar looking stuff can also be suit, on a brick wall, was there ever a furnace/heater/fireplace in that area?

We have a problem with too much moisture in our home and the condensation build up in the winter is rotting the skylights wooden frame. 

Modern condensing boilers are absurdly efficient. 

as it relates to Airconditioners down south the culprit is condenser theft.. you can always tell the quality of a neighborhood if the condenser units have cages around them. 

Many Memphis properties require a cage to keep AC condensers from disappearing.