Tom Tancredi :
That isn't a 'hardware' issue (the video card) that is a software issue (Windows Kernel is the main 'code' of Windows itself). The problem is a issue with Windows itself is corrupt or the hardware (hard drive, RAM, CPU or PSU providing the power) that provides the code / interpret the code is failing.
The first step would be to open a CMD prompt as ADMIN and do a SFC / SCANNOW to ensure the files are not coirrupt. After that I do the 'basics':
Did you install all Windows Updates? Including OPTIONAL except BING? Check them and repeat till ALL are installed.
Download and run Slim Drivers, install all the latest updates but you don't need to reboot until you do the last update
Download Malwarebytes do a full system scan (AV doesn't pick up alot of malware) - this resolved almost ALL other similiar posts to date as most had Malware the AV didn't pick up.
Remove whatever AV your using and go to www.filehippo.com and download AVIRA, AVG, Comodo or Panda and do a full system scan - this repeatedly has resolved alot of people issue relying on MS Essentials.
Repeat the AV/Malware scans till the system comes up clean.
Download and run SPECCY, copy and paste the first tab to show your idle temps?
Open Computer, Can Air dust out the bunnies and use paint brush on the vents, coolers, fans, etc.
PLEASE don't respond "did that before" we are working from the point of this post forward, so please DO the steps outlined from the time you read this so we have a 'median model' you / we can work off of we know resolves 99% of the issues out there.
That said: I see your running DDR2, considering that hasn't been used in almost a decade (goes fast!) , and that would inturn mean your running a very old legacy system. Hardware is only warrantied for 3 years, afterwards it will FAIL, given the age of your system, that it can't be supported anymore, and is incompatible with current Consumer Off The Shelf (COTS) products (It can't handle 4K HDDs, it can't use DDR3 RAM, etc.) it would time to VERY much replace the system. Especially with prices so low now for hardware. Broadwell i5 with 8GB DDR, 1TB HDD, $349+ www.slickdeals.net, then swap PSU for 600W+ depending on the GPU you want to invest in $99 at www.pcpartspicker.com, as the 670 you have won't 'cut it' anylonger and need at least a Nvidia 760 or go AMD R9s which basically adds on from $199-$1099 depending what you 'buy into'.
Again that is based on adding to a mid range PC for normal tasks, into making it a 'gaming rig', unless you have other 'normal' uses for your PC which you didn't state.
I have done all of your steps, and nothing seems wrong. Here's the copy-paste from SPECCY:
Operating System
Windows 7 Professional 64-bit SP1
CPU
Intel Xeon E5430 @ 2.66GHz 38 °C
Harpertown 45nm Technology
Intel Xeon E5430 @ 2.66GHz 39 °C
Harpertown 45nm Technology
RAM
8,00GB FB-DDR2 @ 332MHz (5-5-5-15)
Motherboard
TYAN Computer Corporation S5396 (LGA771) 48 °C
Graphics
IPS277 (1920x1080@60Hz)
2047MB NVIDIA GeForce GT 630 (Sapphire/PCPartner) 51 °C
Storage
69GB System-mirror (RAID)
931GB Data-stripe (RAID)
1863GB Data2-Stripe (RAID)
Optical Drives
DTSOFT Virtual CdRom Device
PIONEER DVD-RW DVR-112D ATA Device
Audio
Creative X-Fi Audio Processor (WDM)
Please note that I am temporarily using a GT 630, because my GTX 670 is being repaired.
Side-note: GTX 670 DCII OC should be able to 'cut it', and the difference with a R9 280X is not at all huge, especially when you overclock it (again)
If you know any other solution please let me know and thanks for the detailed answer!