27" inch iMac Thunderbolt Display won't turn on

You could try running a Thunderbolt 1/2 cable into the Thunderbolt daisy-chaining port of the Thunderbolt Display, bypassing the permanently-attached cable.

But that won't help you if the logic board on that old Thunderbolt Display – a display that Apple sold between July 2011 and June 2016 – is going out.

If that is a Thunderbolt Display, it will have a set of ports in the back like those shown in this thread:

Can I just get a new cable for my old Thu… - Apple Community

You cannot remove the permanently-attached cable, but you can leave it unused, and run a Thunderbolt 1/2 cable into the port marked with the lightning bolt symbol. Whether it will fix your problem, I don't know, but people have reported that this sometimes fixes things when the problem is that the permanently-attached cable is flaky or bad.

If your Thunderbolt Display has developed logic board problems, that's a different matter …

the author described this display as:

"my 27" Inch iMac Thunderbolt which I have been using as primary display"

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I am not sure you are both talking about the same display -- based on the pictures I think this is about a 2015 iMac that accidentally has ThunderBolt-2 inputs, pressed into service as a display.

Good catch. The OP might be talking about a 27” iMac, from before Late 2014, running in Target Display Mode. If so, there is no way to use Target Display Mode if the Mac is not able to power on - and failure to even power on would strongly suggest hardware failure.

Target Display Mode lets certain old iMac act as displays for certain other old Macs. iMacs do not have any cables permanently connected to their Mini DisplayPort or old-style Thunderbolt ports … and you must be able to start up an iMac all the way to the point where you can use it as a standalone computer before you can use the special key combination to put it into Target Display Mode.

Use your iMac as a display with target display mode - Apple Support

A Thunderbolt Display is a standalone display with a permanently-attached hydra cable that has two heads: old-style Thunderbolt and MagSafe. You cannot run programs on one, and there is no special key sequence to make the standalone display act as a standalone display.

Which of the two do you have?

Sounds like you've given up on the "display" and plan to send it off, or take it somewhere, to be recycled.

Wait -- that thread is not about your ThunderBolt iMac,

That's about a stand-alone ThunderBolt DISPLAY.