Re: generalized question

With the cover off, use a voltmeter to measure the DC voltages on the connector from power supply to main board when powered up.  I don't have a picture reference or circuit schematic to know how the power is routed from the supply to the various logic and analog boards, so this is just a guess.

 

 There should be +5 Volts DC for digital logic and likely +/- 12 to 15 volts DC for the analog circuits.  Current should be 2 to 3 amps for +5V and 0.5 amp for  +12 and -12 supply - to be most accurate, rig up an ammeter on each supply line (custom wire harness).   Or maybe the supply has a part number that you could find a spec sheet with the details - maybe the specs are printed on the supply itself?
 

 From the manual specifications on the power supply AC input:
 Power:  100-240 VAC, 50/60 Hz, auto-switching supply, less than 30 watts consumption

  So with 80% efficiency, there is ~ 24 Watts DC output - taking a guess  5 V @ 2.5 amps,  +/- 12V @ 0.5A each  ==> 12.5 watts + 12 watts = 24.5 watts
 

 Buy a replacement switching supply with these same output voltages and  same (or greater) current ratings having similar dimensions and replace.   You can find switching triple out supplies on eBay for $20 to $30  shipped.  This may require some custom wiring and mounting to get it to fit.
 

 Or you could try repairing the supply - remove it and inspect for any burnt or leaking/swelled components?   Something must be out of spec and after time it warms up and starts to work?
 

 Is the warm up required each time you apply power?   If you briefly shut off and power on, does it still take same delay to power back on?