were you using any unbalanced TS or RCA cables? or an unbalanced patch bay? that's usually the culprit IMO. Get too close to the computer (which generates a lot of EMI) and it picks up noise.
consumer/desktop UPS won't do voltage regulation unless they specifically say that in the specs. they usually have minimal filtering which may be enough - or it may not. Its likely not much better than your average surge strip even if they "claim" to protect against lightning. That's just complete marketing BS because if you really get hit by lightning that UPS will simply melt (if it doesn't explode). It will protect you from sudden power loss and it might protect you from a brownout, but the voltage has to sag to whatever the UPS's preset threshold is (usually ~+/-5%) before its going to kick over to battery backup via the inverter. some more expensive UPS's have a "sensitivity" switch that allows you to have a little control over how quickly it switches back. if you really have noise issues you need transformer power unit. if you go that route, check the capacity - it won't be much for most consumer units (like UPS's...).