No one thought about the damage the moisture in the place would have done.

Around a month ago our tenants started complaining about it being hot inside the home with condensation and potential moisture problems.

Left California for a market I could better penetrate. 

Is there a simple way I can cover the chimney up so rain/moisture doesn't get in but also allow proper ventilation?

If it's moisture creeping in from the ground, consider adding a dehumidifier or figuring out how to seal the basement.

Also, people with sufficient funds will leave these areas and the area will go into decline.Climate - Properties in areas with hard freezes and excessive moisture will tend to require more maintenance than in milder and dryer climates.Age of the property - The older the property, the more maintenance it will require, unless all the major systems and components have been updated recently.Property cost - There is a tendency for new investors to choose locations with very inexpensive properties.

Would we need to do a test inside the wall to look for moisture? 

What pattern are you using, does underlayment need to be put down, do I need a moisture barrier etc. 

The property needs some foundation/moisture mitigation work, a trash out, and a full rehab.

Current issues: - potential roof penetration-plumbing do to leaks -cabinets (there was a leak under the sink and 3 drawers aren't working, do I price for a new set of cabinets?)