Is there a way to diagnose an iron problem at home?

Question

Iron

Packard Bell EasyNote LS11-SB Notebook: AMD Quad-Core A8-3520M APU (1.6GHz; Turbo Core 2.5GHz, 35W) / 12GB / 750GB + 500GB / DVD - RW / Radeon HD 7670M (128bit) + Radeon HD 6620G (1GB) / Win10 / 17.3" / Li-ion battery 10.8V 48 Wh (4400 mAh) - Purchased in December 2012
November 2013 - Blue screen of death, with a link to the video driver.
Consequence: external monitor is not detected automatically through VGA (manually detected), via HDMI it is detected, but it is impossible to set the refresh rate of the screen, the default is set to 60. Replaced the thermal paste
November 2014 - The buttons on the keyboard started to burn.
November 2015 - An external monitor is not automatically detected via VGA (also not detected manually) and HDMI (Manually detected), it is impossible to set the screen refresh rate, the standard is set to 60 by default. The battery began to support the life of a laptop for 25 minutes instead of 1 hour 27 minutes. After a couple of days, the state of the laptop returned to the time of November 2013. If you turn on the laptop and close the mug, the OS will boot with the screen turned off - there is no image, the laptop is working. Allegedly, there was support for changing the screen frequency, but it still did not work properly.
AMD Dual Graphics stopped working, the speed in games dipped, although what it was for the past two years is unknown, since they did not start.
January 2016 - After updating the drivers, the temperature of the video chip rose from the norm of 55 to 80 degrees. Blue screen.
Consequences: it was possible to set the refresh rate of the screen, which allowed the external device (projector) to display a 3D image. Hooray ;-)
February 2016 - After updating the drivers, got a blue screen. You can set the frequency to 120, but the FPS sank to the baseboard when displaying a 3D image, artifacts appeared. Launched GTA 5 - a ton of artifacts in textures (disappear), although everything works quickly, I did not launch other strong games.
March 2016 - Replaced thermal paste, temperature dropped from 65 to 40 without much load and from 80 to 70 under load test. One of the thermal tubes at the video chip was soldered off, I did it as it was. A 5200 mAh battery was purchased, in AIDA it shows 4800, the original was at 4400. The operating time is 38 minutes.
Questions:
1) Is it possible that the problem is not only with the video card? Is there a way to diagnose the problem at home? Is it possible to solder (in the service) to something else?
2) The Chinese again turned on the heat or the battery is discharged due to problems with the laptop?
PS Under the 3D image is meant the output of a stereo image to a 3D projector

Answer 1

1) Not only with the video card but also with the drivers. Replace the thermal paste, run it disassembled and see if you can’t feel it with your hand, is the cooling fan working?
2) The Chinese always give heat and put glass into the batteries instead of the necessary materials