Try another set of batteries. You already speak out your doubts about the "fresh" set. If they're rechargables and have been lying for too long, voltage may well have dropped below the critical level despite the fact that the batteries haven't been used.
As far as I know, you can't brick any handheld by replacing the batteries when the switch is on. The moment you remove the first battery, it's the same as putting the switch to "off" and when you replace the last battery, it's the same as putting the switch back to "on". Nothing more.