How to tell if Graphics card is dying?

Usually you will start getting regular crashing, artifacts and lines all over the screen and stuff like that.

Paul

If your video acts up, it's sometimes the PSU that's actually the problem and not the video card.

Also, at least every 6 months, you should clean the heat sink/fan on the video card, and reseating it couldn't hurt.
[Can of compressed air with power cable removed if you don't want to remove the card, plus I use q-tips to slowly remove any gunk I find on the fan(s) and in the heat sink.]

Also, the thermal paste MIGHT be issue between the GPU on the video card and the heatsink/fan assembly, they don't use the good stuff as a general rule, so if the card is older, that is a very strong possiblity.

$10 and less for good thermal paste, example here: [4 grams is enough for many uses, doesn't take much]

ARCTIC MX4 Thermal Paste - 4gram - Newegg.com

If you get sudden BLACK SCREEN computer OFF death, that can be PSU or motherboard failure, not so likely video, sucks having to troubleshoot, but that was my last failure; was motherboard.

Easiest is a PSU tester, takes a matter of seconds, otherwise you swap it out for a new one.

Not expensive, example:

APEVIA PST-03 Network/ PC Service Tools - Newegg.com

A local repair shop can test it for you, call around and ask for a free PSU check.

If not really your thing, I would call shops and ask them what their fee for troubleshooting a problem is... remove the hard drives and take the rest if you do, so no data is at risk AT ALL. :)