Your power supply is probably broken,
high pitched noise is usually one of best signs that could indicate that PSU is going to broke or already broken.
Pressing power button many times also speaks toward broken PSU case as when you press and release button it will discharge capasitors and then immediately charge them again, doing this many times could still make almost broken capasitor to work once again for some moments.
If you want to check PSU first
then go ahead, here is few things that you may want to look for after removing protective covers from PSU:
Check if there is burn marks anywhere, check both sides of circuit board.
Check for broken / blown capasitors (all three is going to blow up):
As you can clearly see its usually (but not always) pretty easy to visually determine broken capasitors. Capasitor top cover should be flat, yes flat and that flat is completely flat.
If you have some experience (or someone with experience) with multimeter then you could use it to test some parts or if you happen to have oscilloscope then you can use it to diagnose whole PSU and/or defective parts.
Actually, I'm trying to tell that your PSU is almost dead
at least every aspect in description of your problem is telling that some of power circuit capasitors are failing. There is also other power regulation circuits in mother board, mainly supplying power for CPU but usually if they are broken it may start up fans and maybe flash some lights and then immediately go down again.
Thanks to Power Jack Repair I figured out how the loose power receptacle on my Lenovo 20266 laptop is related to this Lenovo no response power issue. I've had this EXACT (Model 20266) Lenovo laptop since 2014. Since that time, the female power receptacle on it has broken twice. Each time, prior to having the laptop repaired, I continued to use it which required me to finagle the male portion of the AC adapter's power receptacle inside the female portion of the laptop power receptacle in order to get the laptop to take a charge. All the while doing this the connection would get looser and looser to the point it would hardly work (connect) at all. The danger in finagling the male and female power receptacles this way, is that doing so bends the pins a little bit at a time each time you do it and this may cause the pins to touch within the female portion of the laptop power receptacle which in turn may short out the motherboard (MB) or as I finally figured out it can also cause the power cycle process of the laptop, which is controlled by CMOS, to become confused.
In my case, each time the power receptacle has been broken like this and I've finagled the power receptacles (before having it repaired) to get the laptop to take a charge, the laptop has gone dark. Each time this happened, I initially thought I had shorted the MB. The first time this happened, I sent the laptop to Lenovo for a MB replacement, but Lenovo got it to work again without replacing the MB; however, as is typical with Lenovo, they didn't tell me what the problem was or how to fix it or address it. The second time it happened, I thought I had blown the MB again - because Lenovo never told me it had not been blown the first time - so I called Lenovo to get the MB fixed again and they said "your out of warranty and on your own". Needless to say, this is the last time I'll buy or recommend Lenovo.
So looking for a solution, I found this awesome video https://www.youtube.com/watch?v=2yjPUOnAqP4 from the guy at Power Jack Repair and hearing the comments at 0:40 (about the pins touching inside a broken power jack) and seeing the comments posted on the screen at 32:20 (about how to reset the laptop when it is confused about where it is in the power cycle - power up and power down properly - process) I was able to put 2+2 together; the fact is, I had not shorted out the MB. I looked at the pins in the female power receptacle (as in the video at 0:40 mark) and could see that several were touching.
So, WITH THE INTERNAL BATTERY UNPLUGGED FROM THE MB, I used a screw driver to separate the pins. Then, following the instructions on the screen at the 32:20 mark of the video, I had already opened the back case of the laptop, and I had already unplugged the battery connection to the MB. So then I unplugged the CMOS battery which is the round battery in the upper left of the opened laptop. Then I left these two batteries (the mail battery and the CMOS battery) unplugged and let them sit for an hour unplugged which allowed all the power remaining in any circuits to drain.
Then, after that hour, I plugged them back in and put the cover back on the back of the laptop and then I plugged the male power receptacle of the AC charger back into the female power receptacle of the laptop and finagled them to get the laptop to charge. Then, I let the laptop sit and charge for about an hour. Then, while it was still plugged in, I pushed and held the power button for about 70 seconds (the Power Jack Repair guy says to hold the power button in for 64+ seconds, so I did it for 70 seconds) and after releasing the power button, I left the laptop alone - pushing no other buttons - and just let it sit there. Then it reset itself and it came up to the login prompt in about 30-60 seconds. Thanks to Power Jack Repair. So the pins touching "may" short the motherboard, BUT it "may" also confuse the laptop and cause it to go dark and lose it's place in the power up and power down cycle which is stored in CMOS and other circuitry inside the laptop.
Best Answer
I think it is probably useful to understand how and why a controlled shutdown and startup helps. With computers, a proper shut down lets it flush out whatever's on the disk. With most other devices, the idea is to try to avoid inrush current damaging the device as power flows into a newly connected circuit.
If a device is sensitive to such things its probably designed to handle it to an extent, and if you switch off things properly (first the device, through whichever proper method suggested by the manufacturer, then the power supply, and switch things on in the reverse order), things should be fine. Yes, its more work, but its the best way to avoid damage
I would however change that power adaptor. High pitched noises indicate a fault somewhere, possibly a VRM whem its not under load. This might be a bad thing.