I think I'd ask what's changed
Have you plugged in any different devices? Have you changed power connections? Is everything connected via 3 prong grounded plugs? Many UPSes come with software that'll tell you what the voltages are, have you looked at that? Sometimes a USB device can confuse the POST (Power On Self Test), so I'd try unplugging everything except the keyboard and mouse to see if that helps. If the UPS is over 3 years old, the battery may not be up to snuff, but when plugged into the A/C, that shouldn't keep things from working unless maybe it's absorbed some voltage spikes. They're cheap enough, so you could replace it. As a test when the weather's good and there's no reason to expect lightning or power outages, you could try just plugging the computer straight into the power outlet just to see if it would boot. If you do that, I wouldn't leave it that way for more than just long enough to try booting up.