This sounds like classic Red Screen of Death for the older iPhone models. Its usually a faulty battery connector on the board, corrupted data, or defective logic board.
I would try the restore first through itunes if you can, as that would be the more affordable solution.
Battery connector issues (likely problem with red screens) is a complicated repair that would require microsoldering a new battery connector on to the motherboard. I would have a seasoned tech do this if you don’t have experience with microsoldering.
If these solution don’t work, the board is bad and its time for a new phone.
Good luck