I find that rather strange.
Because when it comes to any type of SSD drive or capacity of the drive, they in fact require much less power demand from the laptops motherboard.
Lest`s presume that without question the laptop allows you to plug in any 2.5" drive that has a sata interface on it.
What would happen if you fitted a mechanical 2.5" drive instead of an ssd drive since the mechanical would no doubt require more current or voltage to run.
Personally I could just not see it happening because it would mean Lenovo did a serious miss calculation on the amount of power the motherboard could feed to connected components to it and would of been picked up in the product design stage.
And end of line quality testing checks.
What I would do though is take a note of the conditions of when it fails to turn on.
For example if just using the battery of the laptop is it when the system fails to power up.
Does it power up every time without any problem when connected to the mains charger and the problem stops.
How secure is the SSD drive locked into the base of the laptop and is there any movement between the drive and the connector of where it slots into on the edge of the laptops motherboard.
Laptops can be a bit fuddy duddy about things like that.
And depending on the bios and the testing procedures it hold or performs if a condition of the testing process fails it can prevent a laptop from posting.
As an example A year or so ago I was presented with a Lenovo laptop to fix.
I spend three hours on it, and took it apart to its bare bones.
Cpu power were all good when tested.
Yet the system exhibited the exact same problem as you are having.
In the end I was fully tearing my hair out trying to work out what the problem was.
In the end I found out by pure what if questioning.
What if I disconnect the keyboard ribbon from the laptop and try to power it up.
Stupid as it sounded, I gave it a go since there was little else left to test.
And would you know it, pressed the power button on the laptop and it powered up to display a post screen image.
memory, hardrives ect all working .
New key board and the problem was fixed.
Now who would of thought a keyboard that was faulty would stop a laptop from powering up??
What it shows is, although you press a power button on the laptop everything is tested to see if it is connected right and functioning.
Bear that in mind and it`s more than likely the case with your Lenovo laptop anguyen128 in some way.
But what annoyed me most is that I would of expected the laptop to give me some sort of error to pin down the problem, that would of saved hours of work something like "keyboard test faliure"
It would of helped a heck of a lot, and saved a lot of time, Cheers Lenovo, for not thinking of this.
And yet so simple to include.
Anyway I would check for thing like that any faulty keys on the keyboard, and how snug the drive is connected to the laptops motherboard via the sata interface, to the power conditions battery, or running on mains.