Check output voltages on the power supply with motherboard disconnected

If there’s anything weird there honestly I would just look into something like this . There are other versions iirc and you can find it cheaper too but basically a drop in psu replacement that uses modern components.

People are talking about recapping and fixing the power supply. It’s honestly not worth it on many of these older systems unless you’re a die hard that insists the hardware be 100% original. You’ll spend 30-50% of the cost of a replacement psu on a recap kit and that might not fix it (I am a big believer that recapping for no reason is a bad idea, especially on old pcbs like this that can easily delaminate). When you factor in potential extra time spent diagnosing and fixing the actual problem (bc it’s probably not recapping) plus the fact that the modern psu will last longer and deliver cleaner power, protecting the motherboard and allowing it to last longer as well, it’s a no brainer imo.

If the issue is on the motherboard then sorry. It’s usually fixable, but harder. This gen of console is an okay place to start learning if you ever wanted to (though what you describe with the whine sounds like psu issues imo). Previous 2 gens are a bit easier tho