In my project Uno with a 2.8" TFT display (ili9341) is being used.Code & display working perfectly when its connected via computer USB.
Today tried with 4.2V Li-ion 1200 mah,Uno got powered up but TFT failed to display very dull Screen(Almost invisible).
(battery measured Voltage 4.19V)
Vin is not suitable to power any TFT display. It has a weak LDO, that can only supply the UNO (plus some small IO output). LDO will further reduce the voltage.
Yes, use a step-up converter to 5V, and connect to 5V pin.