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Why OLED monitor burn-in isn’t a huge problem anymore
(arstechnica.com)
This is a most excellent place for technology news and articles.
CCFL-lit LCDs are so inefficient compared to modern LED-lit LCDs that you've probably spent enough more on electricity by now to have bought a more efficient monitor.
I can't speak to the environmental impact, though. Producing the new monitor emitted some amount of CO2, and powering each monitor takes some amount of CO2 per unit time. At some amount of use, the newer monitor will have lower lifetime CO2 generation than your old monitor.
Not OP but my electicity is <$0.10 / kWh because of where I live. It seems like it would take much more than 13 years to hit the break even point on upgrading the monitor just because of energy efficiency.
Even if the newer monitor has less of a lifetime environmental impact, throwing out the old still working one is still wasteful. It's already made and working. Using it longer lessens your environmental impact. If you repair the old one when it eventually breaks, that's still less of an impact than an extra ~20% electricity usage. Especially since electricity generation is getting greener all the time.