Good Evening fhenry, this kind of problem is consistent with a bad or high resistance negative lead from the battery to the chassis.
Generally the ground lead will go directly to the engine block and another lead will pass from the engine to the chassis.
Check all lugs and connections in this area.
If everything checks OK it can also be cause by a high resistance in the positive power supply to those items at it's source.
You will need a circuit to determine where the actual source is, a haynes manual could be very useful.
Use a meter and ensure +12 volts is available at the underdash fuse holder when the items are switched on one by one.
If a voltage drop more than a volt is noticed check the route back to the battery plus connection possible a fusible link or under hood fuse could be involved.
Feeling all connections in the area should allow the problem to be determined by it being hot with all systems running in that particular case.
Resistance develops heat with current flow and drops the voltage.