Hi:
I don't know what generation Elitedesk 800 you have...G4, G5, but here is the service manual for the G5:
http://h10032.www1.hp.com/ctg/Manual/c06443940
You can find the setting you need to enable in the Advanced menu>Boot Options> After Power Loss. Default is Power Off.
Change the setting to Power on—causes the computer to power on automatically as soon as power is restored.
Save the settings and exit the BIOS.
Refer to chapter 6, page 103.
If you don't have an Elitedesk 800 G5, then please post the generation you have.