You have a few possibilities.
Wake on Lan in a script where you can be notified when a server is correctly rebooted or not.
Almost every recent servers have interface that allows you to connect to the server remotely to manage bios, booting option and remote started. With HP it's ILO:
We have a currently have a set up that use Zabbix. We have it configured to send email when a switch, server, printer is offline. We also monitor our UPS to send shutdown command on all our server, esxi, vm, switches, management console, router, etc when the power level are too low after power failure.
We then configured this zabbix to power up servers in the order we wanted. We can get notification when a server didn't reboot correctly.
Took a bit of work but was worth it.