MacBook Air chime but black screen

I’m trying to fix a MacBook Air that starts up, chimes but goes to a lit gray screen. There has been no water damage or drop. I left the MacBook unplugged a week ago when I left for vacation and came back to this problem.

I’ve tried the following:

1) SMC Reset (when I hold the left Shift+Control+Option and power button, Mac turns on immediately after releasing the buttons)

2) PRAM Reset

3) Tried booting to virtually all modes (Safe mode, Single User Mode, etc.)

4) When I boot to Target Disk Mode, the Thunderbolt symbol shows and bounces around the screen, but the laptop does not show up when connected to another Mac.

5) I’ve tried unplugging/replugging the battery and display cable.

Can anyone recommend some other courses of action to try to save the laptop? All of my data is backed up to iCloud so wiping the laptop is not an issue, I just can’t seem to get to that point.

Thanks in advance