Engine will not stay running, codes P2014, P0113, P2185, P0190, P0798, P0864 and P0841

Yesterday a car owner called and drove me to a garage where the car was parked. On getting there, battery from is Lexus was pulled out and used for my testing in his car. 

  The car that is faulty is listed above. The check engine codes I noticed when I connected my scan tool were: P2014, P0113, and P2185. But when I checked for modules, the codes were: P0190, P0798, P0864 and P0841 were added previous three codes I highlighted earlier.

  Before long, about 7 minutes or less during my scan I wanted to crank the engine over to check the live data and the operation of the car unfortunately the battery went low. 

  Hence, I couldn't carry out more test. In an interview of the car owner about what he used to notice the symptoms in the car and what was replaced in the car in an attempt to solve the problem. He highlighted that it happened on is way, when the car was on motion and suddenly went off. He allowed the car to cool down for some time. When he tried starting it again it started and moved for some distance and stalled out again.

    He invited an electrician to check the cause and fix the problem. The fuel pump was replaced and an actuator as he said but that he can't recall the name at the moment. The car was then driven to a garage where I meet it. Since then, they've been trying to fix the problems permanently but to no prevail. 

  Initially, most of the times the battery will drain out quickly and when car gets hot, the car will go off on motion. But he has not noticed stalling off the car at idle.

    At a point, is oil sump was broken. Consequently, the engine oil was replaced, top cylinder valves grinded, oil switch, plugs, coils, top gasket and PCM were replaced but the problem was still not fixed.

  Moreover, it was also noticed that mostly the car will hesitate whenever it wants to climb hill like a popping sound accompanied with that and move very slowly on smooth road. 

   At present, the man said the car problem have gotten worse, it only cranks but doesn't start anymore.

In summary, the car used to drain very fast, struggle to climb a hill or bump, and when on motion engine stalls when hot.

Please help me out on how to solve the car problems and get the car starting.