I'll help you out with the BSOD issue you're getting.
Code:
BugCheck A0000001, {5, 0, 0, 0}
This bugcheck is unknown, and I've seen it a lot recently.
Looking into it though, it seems to be related to amd display drivers.
Code:
fffff880`0311b718 fffff880`100d47ce : 00000000`a0000001 00000000`00000005 00000000`00000000 00000000`00000000 : nt!KeBugCheckEx
fffff880`0311b720 00000000`a0000001 : 00000000`00000005 00000000`00000000 00000000`00000000 00000000`00000000 : atikmdag+0x277ce
fffff880`0311b728 00000000`00000005 : 00000000`00000000 00000000`00000000 00000000`00000000 fffffa80`1059a000 : 0xa0000001
fffff880`0311b730 00000000`00000000 : 00000000`00000000 00000000`00000000 fffffa80`1059a000 00000000`00000000 : 0x5
All we can see are the parameters which the bugcheck displays being sent along with the amd driver.
This is mostly likely one of two things, either a bad display driver or the graphics card is failing.
Given you also mention a 0x116 bugcheck I'd say your GPU is failing, we can try changing the driver though.
Without a Kernel dump I can't check your temperatures for you but r9 290x GPUs have been causing a lot of trouble, especially due to overheating.
What temperature is your PC at?
Code:
1: kd> lmvm atikmdag
start end module name
fffff880`100ad000 fffff880`10d9d000 atikmdag T (no symbols)
Loaded symbol image file: atikmdag.sys
Image path: atikmdag.sys
Image name: atikmdag.sys
Timestamp: Fri Dec 06 21:19:43 2013 (52A23F6F)
CheckSum: 00CA856E
ImageSize: 00CF0000
Translations: 0000.04b0 0000.04e4 0409.04b0 0409.04e4
I suggest updating the driver to the latest version, if that doesn't help then try a beta driver, if that still doesn't help then you could try rolling back further than December last year.
If changing the display driver doesn't help at all in frequency of the blue screens then your GPU is probably failing.
Either that or you have a bad motherboard.