Wet carpets on closed car over night = fogged windows. Do people really drive around in the rain with open windows? How do you suppose water worked its way uphill to the top of the carpet? Is the wetness slick if you rub your fingers in it then rub the fingers together (the way anti-freeze does)?
What I am saying is throw most of you effort toward the heater core, it is probably leaking. Gravity dictates that liquid falls down from a higher place, the higher place is the heater core.
I am guessing that you are not equipped to fix anything on a car, so you would be well served by seeking professional help.

The water pump lives on the passenger side, in the rear of the engine.

 

Then again a wet carpet could be the result of a clogged HVAC drain.

 

My dad ran some blower fans inside while I was at work a few days ago. Doesnt seem to be any moisture inside the car anymore even after raining and being very condensated outside. I think it's good but will keep an eye on things.

Opened up the valve covers today....timing chain loose...lots of gunk in here. Did they never change the oil or what?

 

Yeah. That engine did not see regular oil changes.

 

Cam lobes look cooked, I’d be inclined to remove the head and clean everything up , replace the head gasket and the timing and the balance shaft chains, the water pump, and the oil pump.
It’s not a hard job, time consuming but it’s worth the effort.

 

All the videos I look up have the engine out of the car...is it easy enough to do with the engine still inside?

 

That's not deferred oil changes, that's oil emulsion, probably combining with coolant.

 

I tend to agree. The cylinder leak down test I mentioned in his other thread might prove it, if it's the head gasket. But it could be leaking at the oil cooler, or internal leak in the turbo, test probably won't show that.

 

Like I said, change the head gasket, and the water pump and the chains. When you drain the radiator, look for oil in the coolant. If it’s contaminated, change the oil cooler and radiator, and hoses, once you clean it up!

in or out of the car not a bad job!

This is for a 2.4 but the 2.0 is similar

http://www.ddmworks.com/assets/image...uild%20Kit.pdf

If you remove the upper engine mount and the bracket for it that gives you more room to get to the front cover bolts. I’d even consider a new oil pan.

 

Need another engine. I wouldn't waste my time on that one. Fix one thing and something else will fail.
That much crude in there will plug up oil passages and galley's. Next will be oil pump then rod and main bearing failure. And I'll bet the turbo is on it's last leg if not shot.