Okay, then my next suggestion is that the pump's head is faulty...They do seem to wear out over time. I have the same pump - it's about 18 yrs old - and it has failed twice. The first time, I emailed Topeak and they sent me a new head for free -- it just threads onto the end of the hose. The second time it started to fail, I happened to be in a bike shop that had a spare, so I just bought it.
So, that's what I would try next, if I were you. Send an email to Topeak explaining the problem, and see what they say. And use your neighbor's pump in the meantime.