The iMac 27 inches mid 2011. Starts to a blank screen .
When started it progressed to a blank screen and stopped
iMac 27″, macOS 10.13
It’s trying to tell you it’s ready to be replaced and recycled!. At almost 15 years it’s not worth fixing even if you can find the broken hardware. When you replace it with a new Mac you can migrate from the 2011’s Time Machine backup.