Another option to look into on restarting the system after a power outage would be Wake-on-LAN. It uses the network to restart the system by sending a "magic packet" to the system.
http://en.wikipedia.org/wiki/Wake-on-LAN
If the pc supports this might be a nice way to restart. Some UPS systems and routers offer this support also ( see below) but if your staying with the current model you could do this manually from a website etc.
more info on router support for this
http://en.wikipedia.org/wiki/DD-WRT
If accessing BIOS isnt an easy option might also contact HP to see if they have a solution for you.