I had the same issue with my Bose mini 1st generation and this happened when it ran out of battery same day of using it. So there is No lights (red,yellow or green) on even when it's on the cradle or directly plug in to ac outlet (Considering the ac adapter and cradle has working status / power), because each time you plug and unplug it, it has a sound thingi..
Ok now - The solution I did while it's PLUG in:
1) Press and Hold Power button for 15 sec (no worries even if you will not see any lights on)-this is the Reset.
2) Press and Hold Mute button for about 15 sec (you will see couple lights will turn on as an indicator your Bose is not busted)
3) Now Press the power (just 1 sec) and bingo!..power lights indicator comes on either a yellow or red (it needs charging). Mine had a blinking yellow.
Seems it went to a protective mode or something
Note: I did this a few times by experimenting and combining 1 and 2 simultaneously.
I hope this helps! Good luck guys!