My display doesn't work

For a while I was limping along using my iMac with frequent blackouts which seemed to repair themselves after a cooldown period.

Later I started using an external monitor and was fairly happy. Then the whole thing went dark. Now it seems to power up but no display either on built-in display or external monitor.

I wish to get my files onto a thumbdrive and also to repair the computer.

Is it the led board? or what?

Thanks for any ideas

Jim