Joeschmuck, the problem with MB settings is that those are based on the computer's power supply turning back on when it senses 120V input. I have the UPS set to shut the machine down after 10 minutes, but in reality it could probably keep it running for more like 45 minutes (it's only a 1500VA UPS). So using the motherboard setting, it would probably re-start immediately since the UPS would still be outputting 12oV to the PC, then it would run for another 10 minutes until the timer ran out again, and so on until the battery died. Maybe this isn't the case, correct me if I'm wrong. Also, I didn't see any settings on the MB menus anyway (ASRock, Z77 chipset), which is weird because my circa 2005 machine from college even had that setting.
I didn't know if there was another way to do it. The reason I'd like to to re-start automatically on power-up is that it's hosting the website (Apache plugin) for my side business. (I know the next suggestion will be "you should get a hosted solution for your website" but it's not urgent enough to spend the money. I had the server/UPS before I started using it for hosting a website, hence not trying to figure out auto-reboot previously.)