Lenovo Ideapad S400 turns off when booting into any OS desktop

[keepread]

I've been using this laptop for quite some time w/o battery. It has Linux installed. Recently, someone sent me a web link in an instant messenger. When I clicked on that link the laptop turned off that instant, before the browser even loaded to open it. Since then it turns off several seconds after I start it up and log into the Linux graphical desktop. I can see the mouse cursor moving around the screen when I draw my finger on the touchpad or move the mouse, and then a terminal window begins to load because the desktop autostarts it from last time, and then I hear a pop from the speakers and it shuts off that instant.
If I do not enter my Linux credentials, then it stays on for however long I want. If l switch to text console, say by pressing Ctrl-F2, and enter my credentials, then I can work in the text console for however long I want.
I tried to move its SATA SSD to another machine. There, it boots and works fine.
I tried to put another Linux SSD or HDD in this laptop. Both shut off as soon as the desktop begins to load, usually when the background showed but prior to any panels.
I tried to boot from a Windows USB stick, but it shuts off before anything is displayed on the screen.
I tried a different known working memory stick. There is no GPU or video memory on the mobo, so IMO this rules out bad memory.
Unfortunately, there is no BIOS update on Lenovo for this model, so I cannot try to reflash the BIOS.
Out of ideas at this point.

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Going out on a limb, but it feels like the PS is too old. Unfortunately it is the only one with the compatible plug.
Have lots of known good Dell PSs. I would like to try to get an adapter from Dell PS to Lenovo power socket. Any tips on what type exactly I should look for?

Lenovo's plug measures 5.5 OD and 2.6 ID which sounds like the 5.5x2.5 plug, but they have yellow tips in the catalogues.
Mine has the black tip, but in the catalogues they have 5.5x2.1 nominal size. So I am confused.

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Turns out that a worn plug was the root cause. Out of desperation, I used a paperclip to bend the blades of the plug back towards the center, and the laptop works fine. They looked too flush with the groves in the plastic, whereas other PS's plugs had them more prominently sticking out of their groves. Whew!

Still looking for help with determining the correct adapter size from the Dell plug.

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Get a new Linux ISO installed. Get a bootable USB drive from a Linux ISO file. Sometimes this overrides the existing Linux kernel installed.

What would the purpose of that be? How is that going to help a worn power plug?

[Echoeye83]

Oh must have gotten the messages late and not seeing that you found the root cause. Sorry about that I was trying to help with the 1st message you posted.

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Please do not feel sorry, Echoeeye! Thanks for trying to help!