I figure the power supply is not unlike a PC power supply with 12v and 5v lines. The 5v line on a PC is for the motherboard. Whereas the 12v is for the peripherals.

So I'd also guess that the 5v part of the power supply is toast. The whirring noise could be the CDROM part spinning up. Like PC cdrom's I expect if a CD is inserted the mechanism automatically queues the inserted data or music CDROM. I suggest pulling the top off the PS1, and pushing down the "cover closed" button normally pushed by the top when you close it.

Once you've pushed the button down, connect the power lead and turn the power point on.

Is it the cdrom part that whirring??

Next move would be test the power supply part. You might find some P/S output/wiring info on the net. Yes, you'll need a multimeter to test this.

Cheers,
Chris.