Black screen of death 2 hours after screen replacement

Hi, my phone recently suffered some water damage, went into a black screen of death mode (backlight slowly died over the course of a couple minutes). For a day, the phone still worked (i.e. alarms/calls rang on vibrate). However, it eventually bricked. I tried connecting it to iTunes for a backup but the “To allow access, please respond on your iPhone” message came up.

Got a new screen put in from a local repair store. I’m not sure if they disconnected the battery while putting the screen in. However, my screen came on, and I set up Assistive touch, intending to get home and immediately back up my phone. By the time I reached home, the backlight once again died away mid-use. The phone remained on. However, when I connected it to iTunes and got the “To allow access…” message again, I tried a hard reset. Didn’t work, phone won’t turn on now.

Is it the backlight filter? If so, does the fact that it worked for 2 hours mean it’s not irredeemable? Can I do a home repair? I don’t need to permanently save this phone, just get it on long enough to back it up. Any advice appreciated!