I had guys quoting me $240 to replace a $10 humidifier line a few wks back.  

An uncommon but possible scenario is a  humidifier installed in the hvac system that is malfunctioning or was turned the whole way up.

Basement - a couple of things 1- is not completely dry has humidifier that I turn on now and again to lower moisture as floors (concrete) can get some water in it. is this a problem for a rental?

My first thought was a room humidifier.

Do not buy them a humidifier!

I don't know how much rain you guys get but the owner had a large de-humidifier he had been using for over a decade and claimed was sufficient except when they had a lot of rain.

Many basement require that a de-humidifier be constantly run. 

Get the carpet treated as quickly as possible, if it's worth saving call the carpet people out, they will extract it  loosen it up in a corner or 2 and put in humidifier's .

The wholesaler mentioned the sump pump broke, which explains the puddle of water in the basement in the photos and the humidifier, but on zillow I found a note that stated "the homeowner had major problems with sewer and flooding" which obviously sounds a bit scary. 

I have two de-humidifiers to help out with that.