Sounds like an internal problem. You have eliminated the battery and maybe the adapter. You need to verify the adapter plug has the specified voltage on it either by measurement or substitution.
Replacing the battery should have powered it on. Most batteries are shipped with at least 50% charge.
The blink of the button LED is telling me there is an internal short and the power module is disconnecting as soon as it detects that.
It could be anything, but a shorted CPU is not uncommon.