iPhone not booting, charging turns it on but it goes backlight black.

I got this problem out of blue, iPhone was working and then it turned off, no wheel, I thought it could be low battery then I tried to charge, It turned on showing Apple logo for like 1 or 2 seconds and then backlight black, and when I removed charger it turned off immediately. I brought it into a friend who fix iPhones and he tried changing display and battery, no use, he told me to try to format it, and I tried, i connected it to my mac but it does recognize, it only recognizes when I put it in recovery mode, mode in which in this case shows no response on the screen, the mac tries the process of recovering, but it gives me the 4005 error.

Would anyone have any ideia what I should do?