I'm a bit confused here. A Black screen with a moving curser would imply you have PCH or CPU level problem. Then you talk about getting PPF003 & PPF004 errors which are the fan's. But, if you can get into diagnostics then the PCH & CPU are working here!
So lets back up here a bit... Did you spill something into the the keyboard and/or trackpad and/or sit the system down on a wet surface? I'm suspecting you have liquid damage here (It could have happened a while ago).
If you didn't get the system wet did you have your system served at some point? I think you'll need to open the system up so check the connectors and inspect for dust buildup on the fan's and fins. Using a soft paint brush carefully scrub the logic board, fan and the heat sink fins then use some can'ed air to blow the junk away.
You may want to get a more informative tool here: TG Pro. It will give you a better idea on whats happening for less than $20 its well worth it!