A couple of thoughts Carlos. Li-Ion and Li-Pol batteries are the same basic type of unit and can be used interchangeably [mostly]. In fact many batteries marked Li-Ion/Lithium-Ion are Li-Pol as the full name for Li-Pol is actually Lithium-Ion Polymer. Li-pol are lighter, mainly because the cells don't need a metal case as li-ion do.

I'm a little suspicious that your unit sprang back to life for ~five minutes. Your new battery has full voltage of 3.7 so the problem must be in the device itself and it seems to have been intermittent at least until now.