The Rx580 was originally released in March 2017. So not quite '10+ years old gpu' unless my math is totally wrong.
Physical age has little bearing on lifespan. I have a 3dfx Voodoo2 3000 16Mb that still functions just fine (1998). Use and/or abuse will determine a gpus effective lifespan much more than physical age.
The Rx580 is still a very respectable 1080p card, absolutely nothing wrong with its ability so it's of far greater value than 'an idle pc gpu' and is a good match up for a Ryzen 3600.
With today's unrealistic and frankly abysmal pricing on gpus, the Rx580 is absolutely worth saving, not everybody has access to or a need for a 3080-3090/6800XT just because they are the strongest gpus on the mainstream market.
Op has a reasonable concern and that demands a reasonable answer and/or reasonable advice.
@osborn12341
Your motherboard has functional led lights in the top right corner that cycle during the boot process. Do those diagnostic leds hang up on a specific led like VGA or CPU or Ram? Or does the boot process finish fully and you are actually in windows but with no display at all? Does the monitor input match the cable used from the gpu?