"Video TDR Failure" Intermittent BSOD

I've had this problem for a couple of months now. Most often the BSOD gives the stop code VIDEO TDR FAILURE, from atikmpag.sys.

But I have gotten VIDEO SCHEDULER INTERNAL ERROR. And from ddkmd.sys.

I did think at one point that it was related to coming back from Hibernation or Sleep, but sometimes I get a BSOD when it's booted from a full shutdown. Often happens when I open a new graphics-intensive tab or have been watching a Youtube video for a few hours, things like that.

I have tried to use WinDBG, but it's just too low level for me to figure out on my own. Would love any help you can give.

[Edit] There are other symptoms that have appeared around the same time which could be related, all indicating the graphics card bugging out. Sometimes the screen goes black while everything else works fine (audio, keyboard, etc.). Sometimes the mouse still works somehow, sometimes it lags severely, sometimes it just completely freezes.

Just now I was trying to use ffmpeg. The machine kept doing that blank-screen freeze until I tried doing nothing but doing the ffmpeg task straight after I booted back up. Then it worked okay.

Start with updating your AMD graphics drivers.
Your drivers are from
atikmdag Tue Jan 13 17:48:21 2015 (54B54C55)
atikmpag Tue Jan 13 17:20:43 2015

Also update or remove.
networx Sun Sep 27 18:21:06 2015
Driver Description: NetWorx
Driver Update Site: NetWorx : bandwidth monitor, connection speed test, data usage log

Your AMD gpucard Graphics Card: 1024MB ATI Radeon HD 4800 Series (Sapphire/PCPartner) is a so called legacy card by AMD.
And you can not use the newer drivers.
And you have already the latest avaliable drivers.

Reading your EDIT i suspect your GPUcard could/is dying on you.
Or are you overclocking or is your system overheating.

You could test your gpucard.

Videotest Furmark
To test your GPU you can use Furmark see this tutorial FurMark - GPU Stress Test - Windows 10 Tutorials

FurMark Setup:
- If you have more than one GPU, select Multi-GPU during setup
- In the Run mode box, select "Stability Test" and "Log GPU Temperature"
Click "Go" to start the test (Looks like it's "BURN-IN test" now)
- Run the test until the GPU temperature maxes out - or until you start having problems (whichever comes first).
NOTE: Set the alarm to go off at 90ºC. Then watch the system from that point on. If the system doesn't display a temperature, watch it constantly and turn it off at the first sign of video problems. DO NOT leave it it unmonitored, it can DAMAGE your video card!!!
If the temperature gets above 100ºC, quit the test - the video card is overheating.
- Click "Quit" to exit

What you are looking for:
- excessive heat from the GPU (report back with anything over 90ºC)
- problems with the video display (picture is distorted or jumbled, picture turns black, etc)
- problems reported by the program (I haven't seen this, but "just in case")