Old mac running High Sierra will not boot - not even in Reovery Mode. WhaT SHOULD I DO?

If your Mac doesn't turn on - Apple Support

1.. Shut the machine down.

2.. UNPLUG the power lead to the computer and any peripheral devices.

3.. leave it for 10 minutes.

4.. Hold power Button in for 10 seconds

5.. Connect everything back up and restart. 

You do not say how old your Mac is. I am guessing that your hard drive has died. Why not take it to an Apple authorized service center and have it checked?