BSOD lately usually just after boot-up

Hiya and welcome to SevenForums!

The problem is caused by your graphics driver. Run Display Driver Uninstaller(DDU)
Make sure you tick the Uninstall C:/AMD and C:/NIVIDA folders while you are in DDU when you are done running DDU install your graphics driver again and you should be good to go! This is the guide for DDU: Drivers - Clean Left over Files after Uninstalling

Remember to remove Catalyst and only install the graphics driver.

How do you recommend installing the driver? Manually via updating the driver in Device Manager?

Ok. Last night I used DDU to remove the drivers, rebooted and manually updated the driver but did
not install Catalyst.

This morning, I've just turned the PC on and it's crashed - twice.

WhoCrashed:

On Sun 05/07/2015 07:15:10 GMT your computer crashed
crash dump file: C:\Windows\Minidump\MEMORY.DMP
This was probably caused by the following module: atikmpag.sys (0xFFFFF88004EE8848)
Bugcheck code: 0x116 (0xFFFFFA8016D61010, 0xFFFFF88004EE8848, 0x0, 0x2)
Error: VIDEO_TDR_ERROR
file path: C:\Windows\system32\drivers\atikmpag.sys
product: AMD driver
company: Advanced Micro Devices, Inc.
description: AMD multi-vendor Miniport Driver
Bug check description: This indicates that an attempt to reset the display driver and recover from a timeout failed.
A third party driver was identified as the probable root cause of this system error. It is suggested you look for an update for the following driver: atikmpag.sys (AMD multi-vendor Miniport Driver, Advanced Micro Devices, Inc.).
Google query: Advanced Micro Devices, Inc. VIDEO_TDR_ERROR



On Sun 05/07/2015 07:15:10 GMT your computer crashed
crash dump file: C:\Windows\Minidump\070515-16614-01.dmp
This was probably caused by the following module: atikmpag.sys (atikmpag+0xB848)
Bugcheck code: 0x116 (0xFFFFFA8016D61010, 0xFFFFF88004EE8848, 0x0, 0x2)
Error: VIDEO_TDR_ERROR
file path: C:\Windows\system32\drivers\atikmpag.sys
product: AMD driver
company: Advanced Micro Devices, Inc.
description: AMD multi-vendor Miniport Driver
Bug check description: This indicates that an attempt to reset the display driver and recover from a timeout failed.
A third party driver was identified as the probable root cause of this system error. It is suggested you look for an update for the following driver: atikmpag.sys (AMD multi-vendor Miniport Driver, Advanced Micro Devices, Inc.).
Google query: Advanced Micro Devices, Inc. VIDEO_TDR_ERROR



On Sun 05/07/2015 07:06:11 GMT your computer crashed
crash dump file: C:\Windows\Minidump\070515-15927-01.dmp
This was probably caused by the following module: atikmpag.sys (atikmpag+0xB848)
Bugcheck code: 0x116 (0xFFFFFA800CDDD4E0, 0xFFFFF88004E54848, 0x0, 0x2)
Error: VIDEO_TDR_ERROR
file path: C:\Windows\system32\drivers\atikmpag.sys
product: AMD driver
company: Advanced Micro Devices, Inc.
description: AMD multi-vendor Miniport Driver
Bug check description: This indicates that an attempt to reset the display driver and recover from a timeout failed.
A third party driver was identified as the probable root cause of this system error. It is suggested you look for an update for the following driver: atikmpag.sys (AMD multi-vendor Miniport Driver, Advanced Micro Devices, Inc.).
Google query: Advanced Micro Devices, Inc. VIDEO_TDR_ERROR

Hmm, downgrade the driver.

I did that earlier today. Now using driver 13.9.

Upon restarting the PC after leaving it off for a short time, I opened up Firefox (this is often where
the PC would hang, then go to a BSOD) - this time, the screen went black but came back on with
a warning about the graphics card not responding but has now recovered.

No BSOD so far with the older driver.

Hmm, run Furmark. Video Card - Stress Test with Furmark