~$800? New GFX card or total overhaul (whichever fixes a persistent graphics crash)

Hopefully I've gotten this right; I tried following the template as closely as I could. Tl;dr: My graphics card driver is crashing constantly and I'm unable to find a solution that sticks. Given that my PC is nearly 6 years old, I figure it's time to at least change the GFX card where I would assume the issue lies, if not the entire rig. My knowledge of components and the different terminologies is fairly rudimentary, so trying to shop for myself has been a bit overwhelming and I need your help! Thanks in advance for your time!

Approximate Purchase Date: e.g.:
This month (asap)

Budget Range:
~$800 if I'm doing a full overhaul

System Usage from Most to Least Important:
Gaming > streaming > surfing the internet > movies/shows

Are you buying a monitor:
No

Parts to Upgrade:
Honestly not entirely sure what all I need to upgrade. I know I need a new gfx card; I'm not entirely sure if I need to upgrade the cpu, mobo, ram, or anything else. Everything I play has been running just fine until the graphics card began constantly crashing over the weekend.
Current PSU is Antec TP-750

Do you need to buy OS:
No

Preferred Website(s) for Parts:
Newegg

Location:
Stuart, Florida, USA

Parts Preferences:
No preference, though overall I've been pleased with the brands that I currently have given the price of the items and how long they've lasted me. 6 years of good service on a budget is a thrilling return

Overclocking:
Maybe, but probably not

SLI or Crossfire:
Nah

Your Monitor Resolution:
1920x1080

Additional Comments:
A quiet PC and/or one that doesn't turn my tiny room into a sauna would be a huge plus, but it's by no means a dealbreaker. Specific software or games? Hm. A few different Voip programs, Twitch/Youtube, specific games would include WoW, League/DotA 2, osu!, Witcher 3, Skyrim, Mass Effect series

And Most Importantly, Why Are You Upgrading:
This thing's pretty old, and I think it's finally shitting the bed. The graphics card driver is crashing literally at least every 30 seconds, making it nearly unusable. I couldn't find a solution that worked (google turned up hundreds and hundreds of ideas but nothing I tried fixed it). Most seemed to simply say that replacing it was the only sure solution. I suppose it's just about that time. I believe (but I'm not entirely sure) that it's just the graphics card dying, though some people hinted that it could also be a motherboard issue. I'm not entirely sure if I should just replace the graphics card or go ahead and bite the bullet to just do a complete overhaul

Include a list of any parts you have already selected with descriptively labeled links for parts. Please do not post only links.
Mobo: Gigabyte GA-MA790 AMD 790GX
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128398

CPU: AMD Phenom II x4 925 Quad 2.8 GHz
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103656

GFX: XFX Radeon HD 5770 (Juniper XT)
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150447

RAM: G.SKILL Ripjaws Series 4 GB (2 x 2 GB) DDR3
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231277

PSU: Antec TruePower TP-750 750 Watt
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371025

HD: Western Digital 500gb 7200 RPM 16MB cache SATA 3.0
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136073

Case: Antec Three Hundred Illusion Black Steel ATX Mid Tower
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129066

I suppose peripherals don't matter, though it might be of note that there are no additional fans or cooling systems or anything like that in place aside from what came within the case.