If it's a voltage regulator then a place you could start is draw a bit of the schematic before and after it. It would have connection to a power rail and output to something, perhaps memory or the network processor. You can look up what voltages those parts use and what pin has the connection, if you can find the datasheet for it.
If you know this much about it then you can do a parametric search on an electronics supplier website. For example you could filter the search down to only voltage regulators (or other similar terminology) 6 pins, the same physical package dimensions, and if it's a fixed voltage you can narrow it down more from there.
That could produce a list of regulators and you could look at their datasheets to see which seem to have the same pinout as the one you have, comparing the example circuit in the datasheet to the schematic that I suggested for you to draw above.
However this seems like a risk or waste of effort if you must spend great time and buy parts, uncertain if that's the only problem or if (if it's a regulator at all) the IC it is providing power to has failed and that caused an overload failure of the regulator. Wifi repeaters are not very expensive, and another possibility is that it failed because the AC-DC adapter for it failed. A power surge would have to come in through the AC-DC adapter or a network cable if that is the cause.
If the resistors can be traced to that component and included in a schematic you draw, you might be able to consult the datasheet for a replacement part and deduce what resistor values are needed for it to operate properly.
One thing that would help you is to take much higher resolution, clearer pictures with better lighting. A phone probably isn't capable of that, rather a flatbed scanner or camera with a macro mode.
