From your additional information it sounds more like a bad battery with a possible overheat issue to explain why your laptop wouldn't start when you replaced both your battery and power adapter from your Dad's laptop.
The heat from gameplay and age eventually reduce the efficiency of the thermal paste used to transfer heat from the CPU and GPU. I'd recommend blowing out the fan exhausts with compressed gas to try and reduce operating temperatures.
You didn't do anything wrong to cause the battery failure. Some go bad before their time and you did have it for over a year. If you consistently have your system plugged in to AC power, it may be worthwhile NOT to use a battery. See
http://h20239.www2.hp.com/techcenter/battery/Battery_max.htm for more information.
It is DEFINITELY worthwhile to check CPU and GPU temperatures on your laptop. I recommend running HWINFO64 and configuring it to log CPU and GPU temperatures in Centigrade. This way, when you run into the "white screen" issue, you can view the log to see the maximum temperatures that were recorded once you can restart your laptop.
Check your CPU and GPU temperatures at idle (when you've just booted the system and have no applications running except for the HWINFO64 utility. If they exceed 50 C after you've done your best to blow out dust from the fan exhausts, your system may be in need of a repaste.
HWINFO64 will also display information about your battery. What does it report for "Wear Level"?
G74SX-A1 - stock hardware - BIOS 202 - 2nd Monitor VISIO VF551XVT