You don`t Need a fan, in fact a fan will draw up downstairs heated
moist air increasing your utility bill, and bring moisture up, possibly
making different problems. You need passive venting of proper Cu ft for
attic volume , to keep attic nearly at outside temps, above dew point.
What is your attic temp vs outside temp . It should be close together.
You have no moisture barrier? Have minimal insulation ? How many
inches do you have ? where do you live , how cold does it get? What
Zone are you in? It sounds like you are underinsulated with minimal
moisture resistance as well as under vented and bath- sewer not exited.
No moisture barrier means you are bringing up lower level
heat-moisture, in a relativly closed space. Sounds like the attic is a
mold pit, Is roof leaking, if not proper static venting, terminating
bath-sewer vents outside, moisture barrier and insulation are needed.
Who designed , built, this unvented dump, who terminated bath and sewer
vents inside? A real hack for sure.