try removing it from the screen and cleaning the sensor and inside of the screen very carefully with some 99% isopropyl and a qtip and then reinstall and test. if it still doesn’t work then the only repair options involve microsoldering and have a 50% success rate at best
Not a feasible repair for DIY. The digitizer and glass are laminated to the LCD with LOCA glue, unless you have the proper equipment for screen separation, LOCA glue cleaning, and re-lamination, then you will 100% damage the LCD. The entire assembly is $65 on mobilesentrix, call around and see if a local shop will order it for you.
try holding the power button for 10+ seconds to force restart, if still nothing, unplug and replug battery and check for life, disconnect and reconnect the screen connector and check. after you installed the battery and back you had a working display that then stopped working or did you not test display after connecting the new battery?
you need isopropyl alcohol, heat source, and a pry tool. you buy an entire new back cover on ebay for $15, pry up the old one with heat and alcohol, clean the adhesive that’s left on the phone, and adhere the new one down. no idea what your experience with repair is, but for a first time or novice repair this would be the absolute easiest method.
my shop uses mobilesentrix for parts. for the 3a there’s two parts available, refurb and premium. refurbs are gonna OEM displays that have had the glass replaced and Premium is OEM quality. I’ve done the 3a, 3a xl, 4, 4a, 6, and 6 pro using both refurb and premium and they’ve all worked perfectly. if you have a local shop you could have them order the display for you and pay for it, however since it’s a bare screen you won’t have any warranty after you adhere it down.
I desoldered a damaged headphone jack and soldered a new one on. Worked perfectly.