I don't want to spoil your best bet, but I've had a similar situation.
When the battery of the 340 is fully drained, USB charging will not start. You need a charger to get a bit of juice and from that moment on you can charge it from USB. So, if your 340 still has some power you have no problems whatsoever. If it doesn't you'll need to get a replacement. I bought a universal powersupply, checked the voltage and above all, the polarity, and all was good.