Black screen, DFU working, Update on 12.5 , Battery almost dead

Old iPad Air has really crappy battery. According to Coconutbatter about 8% health (new 8827mAh, current 720mAh), but so far working when connected to powerbrick.

Today is just black. So I connected to Mac a try DFU mode. It connected, even able to update to 12.5 and reset to factory settings. But still black screen. Now when connect to Mac, iPad play sound but still black screen.

Now the ultimate question:) Do you think it’s worth to try replace battery? Or black screen is just another problem for fix?