Game crashes for no reason. Video card problem?

Question

Video cards

Bought a video card in December. Inno3D GeForce GTX 650 (2GB) from hands for 4000 rubles. The seller did not want to check due to lack of free time. Of the shortcomings in appearance, there was only dust on the textolite. All protective stickers are in place. As I understand it, during the year of operation (the seller claimed that the video card was used for no more than a year, and then lay idle for a couple of months), the thermal paste never changed. However, the temperature in idle fluctuated at 50 degrees, and during gaming it sometimes rose to 70, which, in principle, is satisfactory. At that moment, I also bought 2 DDR 2 RAM sticks in total giving 4 GB of RAM, and in combination with the old 8 GB sticks. I bought HDD WD Blue for 1 TB.
So that's the point. Games started crashing 2 weeks ago. It's just that for some time the process ends and we are thrown onto the desktop. Subsequent launches speed up this process. Skyrim SE is played for about 20 minutes at the beginning. Then it crashes and after a restart it crashes after 2 minutes. And so less and less.
This is not the case with all games. On the Source engine of the game (at least HL2) it works flawlessly for an infinite amount of time. SPORE also works indefinitely. Checked for load. To test The Saboteur at minimum and Mass Effect 3, which from such presets in seventh heaven with happiness grants 100+ fps. Games crash regardless of load. Mostly directx games. So I put the line between OpenGL and DirectX. That's why I downloaded a lot of toys like SPORE, HL2, CS:GO, Dota II and No Man's Sky. These brothers live and work quietly while Metro 2033 Redux crashes in the fifth minute of the game.
It is very difficult to draw any conclusions. I thought it was the RAM. Tried all sorts of variations of RAM - there are still crashes.
A bit about the technical condition:
ASUS M2N-E-SLI on AM2 socket
8 GB DDR2 type RAM (Kingston)
Process AMD Athlon x64 X2 4800+
Inno3D GeForce GTX 650 (2GB GDDR5)
1TB WD Blue
Cleaned of dust, reinstalled firewood, reinstalled Windows, tested on an abandoned video card Nvidia GeForce 9600 GT, which digests with great pleasure , unlike the GTX 650, all DirectX 9 games without a time limit. Let me remind you that 2 weeks ago I calmly played all the games like Fallout 4, Skyrim, Wild Hunt and other games that are now flying out. I hope someone can tell me what can be done in this case. Thank you for your attention to reading this not a short question.

Answer 1

ASUS M2N-E-SLI

This invisible chipset on these motherboards is problematic (eerily hot, with grotesque heatsinks and coolers). So I would start by checking it out.
Well, BP at the same time.

Answer 2

If it was a matter of RAM, then all the games would fly out, and not the same games, and Windows would fall by itself.
Start by measuring the temperature of the processor, chipset, video card, during idle time, during the game. Compare temperatures across games.
Change thermal paste wherever you can, check all coolers, especially CPU, PSU and video. Case coolers are not so important, although if Ezhyg is right, then it would probably be good to put an additional cooler on the case, or even two (for blowing in and blowing out).

Answer 3

This is the reason why I bought myself a console. Because every time I try to put something on my computer, I have to dance with a tambourine to start this or that game. And now I'm not talking about pirates. This applies mainly to licenses. With that said, here's my advice to you. Choose some prefix for yourself, here for example, https://gamestore.com.ua/ I took mine. Buy it and don't worry. Immediately a lot of problems will disappear.