Alright... I've dealt with this one before - not with a CoolFire 4, but with an eVic VT. It's quite likely that the wall wart you're using is simply too underpowered. I've seen some people bring Wall Warts with an output of around 280 mA. At that level, the device isn't even getting enough juice to power the display to tell you it's not charging.
Run down to WalMart or a local convenience store and snag a wall wart designed for an older iPhone or Samsung phone. It should say its output around 1 Amp. Plug it in and charge it up.
IF there's no nearby WalMart or convenience store, you can try a USB port on your computer, but those are also sometimes underpowered. 1.1 and 2 are 500 mA. 3 bumps up to 900 mA. Downstream charging can reach 1.5 Amps.
IF it still fails that little test, then contact the vendor or Innokin.