DeoxIT - That stuff is expensive - but having a few friends in bands - it's excellent for cleaning switches and jack plugs - removes the oxide layer very successfully.
I also had something called TIC3000 - which I got from Tandy when we still had those shops here - works amazingly well on house switches and car electricals - not sure about PC switches - but a little goes a long way.
Had the same problem with the on/off switch on a Amstrad CPC once. While not plugged in, I switched the button on/off quickly a couple of (many) times.
Thing started working!
I guess the QL reset button is not the same build, but it's worth a try