Welcome!
We can neither see nor touch your computer in this setting, and iMacs have been in continuous production for 23 years in five broad families and hundreds of variants.. It is hard to progress with a question like this without more details.
As the computer won't start, you can get the family and sub-model from the serial number. On newer iMacs the number is on the bottom of the "foot" of the stand:
Once you have the number and access to another internet device, enter the number into this Apple support page:
Check Your Service and Support Coverage - Apple Support
The return will look something like this:
In the example, "27-inch Mid 2010) give the family and sub-model.
⚠️ For security reasons, PLEASE do NOT post the serial number in these forums.
If the iMac is too old, the Apple lookup page may not work. In that case, try this lookup site that does better with older Macs:
https://everymac.com/ultimate-mac-lookup/
Hopefully our knowing more will stimulate some insight into the problem.
Thanks!