iPhone SE power button completely not responding.

I found schematics for your phone, but it's not clear from the signal labelling if the chip you're missing is indeed your culprit. The board layout shows it labelled as U0902, and the corresponding schematic says it's a 74LVC1G34GX.

Here's the schematic for that part.

The data sheet for that component says:

The 74LVC1G34 provides a low-power, low-voltage single buffer

74LVC1G34GX -40 °C to +125 °C X2SON5 plastic thermal enhanced extremely thin small outline package; no leads; 5 terminals; body 0.8 x 0.8 x 0.35 mm SOT1226

And of course the drawing for the connector itself would be useful.

Hopefully that'll give you a place to start; the other thing you can do is to run diode checks on the pins; that should give you a good idea of which signal is at fault.

Alisha (@flannelist), you're more familiar with Apple schematic nomenclature than I am; is the signal labelled "BUTTON_HOLD_KEY" related to the power button or not?

P.S., here's a picture of the are you're interested in taken from the iFixit teardown.