One note about UPS units: I have seen at least one model that, once off, will not power back up unless it senses AC mains power. Most UPS are meant only to give you a few minutes to save your work and power down in an orderly manner, so the intent appeared to be to prevent you from inadvertently booting up on battery power only to die shortly.

Now is the time to determine if the one under your desk works that way.