Hi there,
Those inductors you mention are indeed part of the supplies for the central processor. I would start by measuring whether there is voltage across any capacitor on the output of the step down converters, that is, on the 'big' capacitors near the inductors. IF you do not measure any voltage there, check whether there is voltage on the inputs of the step down converters, that is, on the brown, smaller, ceramic packages near the supply. If there is voltage on the ceramic input capacitors, but not on the bulk output capacitors, that particular supply may be switched of or defective. There usually is an enable signal on the control IC's, check the data sheet.
If none of the input capacitors have voltage on them (after pressing the power switch) you may have failure on the main supply or some standby power circuit. Without a schematic I cannot tell whether the standby circuit is implemented in HW or SW in the main processor or some other peripheral processor.
Happy hunting.