VHS_Tape

PSU degrading and not able to go to its true rate anymore.
as demonix00 said just replace cmos battery.

you can use this to calculate PSU
https://seasonic.com/wattage-calculator or https://www.newegg.com/tools/power-supply-calculator/

1. use only boot drive HDD unplug other 2 HDD still have issues? else proceed to 2
2. use remove video card and use built-in still have issues? else proceed to 3
3. Replace PSU (450 to 500w at least) and plug-in back both HDD and GPU still have issues? else proceed to 4
4. Remove GPU and use IGPU still have issues? if its working with iGPU and crashes with GPU replace GPU, else proceed to 5 
5. MOBO = Dying and wants to retire, replace mobo.

It's overclocked by manufacturer in 90% cases. Use MSI Afterburner and try to underclock it (as much as possible using interface, it not allow you to underclock a lot anyway).

its either GPU or MOBO (motherboard).
mobo probably getting bad caps. (encountered same issue as you in the past, it gave me hours of playing the game WHO'S FAULTY!, changed ram, change gpu, used iGPU, change power supply, change avr, change outlet)

try visually checking the MOBO if it have bloated capacitor.
have you tried cleaning both? probably some dust manage to short something.

if your setup have iGPU try doing heavy task like video exporting as you mention while watching something in YT.
if this fails, and have a spare power supply use it, if it still fails its probably your MOBO.

I used DDU and reinstalled the drivers as you said. I tried playing Division again and it never crashed! Thank you so much!!! You are a life saver!

i'd try to DDU drivers and reinstall them

Reinstall display drivers and update bios is there's an update available. 

HDMI ports have versions. HDMI cables have different "types". They use the same physical port, but you will be limited by the lowest port version or cable type, whichever is worse. From Wikipedia:
So if the cable is very old/bad quality, it might simply not be enough for 4K. OP doesn't mention what resolution the Dell monitor is, so it could be working fine at 1080p, but is lacking for 4K (especially if it a newer LG TV, which supports 120Hz).

Can you test with a displayport cable?
 
It is also worth noting there are different versions of HDMI with different transfer rates and video specifications although they all use the same physical cable.  I don't know if ur problems are resulting from an incompatibility.

I agree with this. You can get a used 570 where I live for 70-90 bucks and a used 2600,2600k, 3770, 3770k for about 50-70 bucks.
 
So your total would be 120-160 which is about the cost of a 580 new that isn't on sale.

hit up ebay and grab a used rx570 and a used i7 3770.  it'll cost less than just buying a new 580 but will be a much more substantial upgrade.

Look for a used i5/i7 - they're cheap and affordable these days

why?
 
also, don't trust bottleneck calculators. you will get a huge increase going from 730 to 580. sure, your cpu will stay at 100% and your gpu will be underutilised, but that doesn't mean you won't get a performance increase or anything will break.

Hey, welcome to the forum!
An i3 3210 CPU in this day and age will probably hold back the RX 580 performance by quite a bit. What doesn't help either is that the i3 is  dual core CPU with hyperthreading. Some games nowadays do not support dual core CPU's in any fashion.
If you can get your hands on a second hand i5 or i7, that would be your best bet.
 
Think a CPU like:
i5: 2400, 2500(K), 3570(K)
i7: 2600(K), 3770(K)
 
Usually the i7 2600 goes for a reasonable price on the second hand market.
If you have a Z-series motherboard, a K variant of any of these might be worth it too, so you can overclock the CPU even further. 
 
Keep in mind the 'bottlenecking'  will depend on the game. A game like CS:GO or Minecraft will inherently have a lot of CPU 'bottlenecking', because it simply uses a lot more CPU than videocard power. But some other games will run better.
What games are you looking to play?