...that the 2.4GHz frequency band of wireless networking gear has ever caused problems for a cordless phone, only the other way around. We frequently get the question of ''Why does my wireless connection to the internet disappear whenever I answer my (2.4GHz) cordless phone,'' but I've never seen asked ''Why does my cordless phone go dead/have burst of static whenever I send an email from my wireless laptop.'' It seems whenever there is a conflict, the microwave ovens and cordless phones always win.
Adding to that, your problematic phone is a 5.8GHz model. That's a completely different frequency band. If there is a radio signal conflict, it should be with a device on the same band, not the 2.4GHz band - unless there is a defect in the radio emitter of one or another specific device that is spilling a whole spectrum of garbage frequencies into the air, but that's a different kettle of fish.
Shifting now to troubleshooting mode - what happens when you turn off your wifi equipment (all of it - router and computer(s))? Do you still get the static on the phone? What happens if you put the 5.8GHz unit downstairs and the 2.4GHz unit upstairs? Do you still get the static? Can you take the problematic set to a friend's house, plug it in there, and make a call? Is there still static? Just some ideas to narrow down whether the unit is bum, or the location you are using it in is bum. I don't think there is interference from your wifi, it is something else.