I was fortunate enough to spot a BCA-MZNH1 stand when it appeared on eBay at the weekend and snapped it up - I have uploaded a photo that confirms that the NH1 definitely requires 6V. I also tested my power supply with a multi-meter and it is delivering 6.15V but not sure what current is being delivered as the multi-voltage adapter delivers 3-12V max 1.2A.
The end result is the same though, the charge light comes on for almost 20 seconds and then goes off (as does the display on the NH1) - I left it on the stand overnight with power connected but still no life from the battery so Jimma's battery re-build is looking the more likely solution as NGY's method is a bit above my technical experience.
One final thing I can try (but I am not expecting the outcome to be any different) in a few days as I was lucky enough to win a job lot of HD1s on eBay that includes a Sony AC-ES608K (6V 800mA) power supply. That bundle should arrive early next week and, in the meantime, I will continue periodically tying to initiate a charge cycle on the NH1 as I have know some smartphones that have been caught in a re-charge loop when they have not been used in a while and the battery has been almost completely discharged and then suddenly contains enough charge to begin a full charge cycle.