VGA led stays red but everything works fine

I have a computer with a Asus Z87-A C2 motherboard and an nVidia GTX 970 connected to a screen using DVI. Up until now everything worked fine.

Recently I have switched to a DisplayPort screen.

Around the same time, I have started to notice that from time to time the VGA POST LED on the motherboard stays lit after the POST sequence, meaning that there is something wrong with the graphic card. But everything works fine, the led staying red seems to be the only symptom.

Also if I reboot the computer, the led will turn off after POST (as it is supposed to be when there is no issue detected during POST). And the issue seems to manifest itself more after a cold boot.

I am looking for any plausible cause or any mean to get some diagnostic data (to check the GPU or motherboard status for instance).

EDIT

I have confirmed that the LED stays on when the screen is turned off. When the screen is just in "sleep mode", the LED will turn off after POST. My screen will turn itself off after 4h of sleep that's why I thought of cold boot issues.

Also the LED will stay red when there are no video cable plugged in the PC. Weirdly enough my previous screen plugged using DVI even turned off was enough not prevent the LED from staying on.

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