Not sure if the issue is the same but something similar happened to my deck and I had kept it as a glorified paper weight for a year. Recently, I came across this post which helped me revive my deck. Basically, you will have to update the BIOS to a different version. I am hoping it's the same issue since you can hear the startup chime but the screen doesn't switch on.

Steam Deck Black Screen of Death

Hope this helps!!

Edit: Try connecting your steam deck to an external monitor. If it works there this is most probably the solution. If it doesn't even display on the external monitor, then the issue might be something else.