1) Pull out the battery, (while you know the battery has charge) then replace it. Press and hold the power button as if you are trying to power the device on. (Does it vibrate?) If yes, then youre screen is likely failing, as that vibration means the device is booting. (Shoul the device continue to pulse vibrate, a seperate issue could be occurring)
2) Continual pulsing of the vibrate motor means the device could be stuck in the boot sequence. pulsing over and over again can imply bootloop, short circuits, or a bad battery,
With these ideas tested, and verified that its not getting power, then you can look into why it would not be powering on.
1) battery:
-the battery could be over discharged, in where forcing current directly into the battery, at the proper amperage and voltage the battery takes could fix your issue.
-The battery could be dead, in which case replacing the battery fixes this issue.
2) Charge port:
-your charge port could have loose connections, in which case, touching up the solder on the pins could fix your issue
-you could have a bad port, in which case replacing the port would fix your issue.
3) Motherboard
-You could have a cold circuit, in which case a motherboard reflow may fix your issue
-You could have a failing motherboard, in which case, a replacement board is in order.