Some things you can do: Try another power cord, and make sure the contacts on the IEC connector are corrosion free. Open the access door, remove the two screws securing the top cover assembly and lift it off. Look for the hidden recessed unmarked green circuit breaker reset button on the back of the power supply and reset it. There is a large multi-section interlock switch you can wiggle vigorously also.
The next things are harder and many screws are involved, get some tape or containers and a marker so you can keep track of what screws go back where: disconnect power, remove the power supply and open it up. With an ohmmeter you can check the power switch, circuit breaker and interlock switch to see that they electrically work.
The next things are harder still: Use a voltmeter across the output of the bridge rectifier from +D101 to -D101 (outermost pins) to make sure the large 200V electrolytic has discharged thru its bleeder resistors. Then carefully remove the PC board. For the Sony RH3-2127 power supply replace C109 47uf 35V, I have seen an open one cause a no start. For the Sony RH3-2101 power supply replace C107 47uF 25V and C108 100uF 50V.
If there still is a problem check the inrush current limiter TH101, it looks like a fat ceramic sitting next to the bridge rectifier. It is supposed to go from 8 ohms cold to as low as .17 ohms warmed up (4A test current I think) in approx 83 seconds for soft start surge suppression, So check that the cold resistance is less than 10 ohms. It is harder to check the warm condition which probably draws less than the limiter spec sheet 4A, but if you make some notes on test points before putting the PCB back you can run the power supply with the cover off connected back to the printer and verify that big electrolytic should have about 155V across it in the warmed up ready to print condition. If you see 155 to 162V, TH101 is not causing excessive voltage drop.
Shorted caps on the output or anywhere on the load side could cause overload shutdown but so far I have not seen shorted caps on my printers.