Replacing graphics card on an old 2007 iMac

Hello all!

I've been using this website ever since my 2007 Intel iMac went kaput the first time, or so I thought. Using the guides on this site, I've been able to repair my computer more than once. Every time a problem popped up, I would use this site to narrow down the possible reasons for its issues, and with a pretty decent amount of luck and these guides, I've been able to successfully repair my computer. Now, I have a new issue and I'm looking forward to tackling it. Problem is, I can't seem to find an answer to my question on the internet nor searching iFixit.

Maybe it's because I'm paranoid and don't want to ruin my computer beyond repair, but I don't feel comfortable taking on this new task until I've received some confirmation that my problem is what I think it is, and that the plan going forward makes sense.

So, my iMac is a 2007 model (all-white) running Snow Leopard.

Specs:

• Model Name: iMac
• Model Identifier: iMac5,1
• Processor Name: Intel Core 2 Duo
• Processor Speed: 2.16 GHz
• Number of Processors: 1
• Total Number of Cores: 2
• L2 Cache: 4 MB
• Memory: 4 GB
• Bus Speed: 667 MHz
• Graphics/Display: ATI Radeon X1600

Lately, it's developed this problem where the screen will go black after some time while playing a video game or watching a video. The amount of time that a video or game can last before the image cuts out varies, and strangely, not all video players cause this to happen. My computer will also, at times, develop black boxes on the screen of varying sizes, as if chunks of the desktop or menu have been erased.

Most games, however, will cause the screen to go black, forcing me to restart the computer. During a blackout, I can still hear the audio but eventually that stops on its own.

The last time this happened, I narrowed down a possible culprit in the PSU. Using a guide on here, I managed to replace the power supply (a daunting task but rewarding outcome!). The issue seemed to have been resolved but the problem has returned. Now, I'm thinking it's my graphics card.

Looking into the issue, I've found guides for later model iMacs but (seemingly) none for mine. As mentioned above, my graphics card is an ATI Radeon X1600.

So my questions are:

Is this issue related to my graphics card?

And if so, what would be a good graphics card to upgrade to that is compatible with my iMac but powerful enough to run games that are new enough but still compatible with my computer (like The Sims 3)?