Well, something interesting happened... I've contacted our account manager at Vodafone NZ and he arranged (thanks!) a loan Smartphone while my one is gone. But before sending this one for service, a friend suggested a test: swapping the batteries. And to our surprise my Smartphone worked just fine, thanks!
I'm not sure what's going on, but it seems that my battery was so flat that it wouldn't charge at all. Also, I have my Smartphone on the cradle and later on a USB charger. Perhaps it can't charge the battery through the USB when it's really low?
Well, not sure, but after connecting the Smartphone to a power cord instead it is alive and working fine again. Go figure...
Again, thanks to Vodafone NZ for their quick help in arranging a loan device...