I also had the problem of the charging unit blinking red/green with nothing plugged in. And in fact both my chargers did, so I figured that can’t be necessarily the sign of a bad charger. And leaving the radio on the charger overnight didn’t charge it up one bit.
I tried the second charger, though (exact same model), and it went to red when the radio was put in the cradle (as it should, to indicate a low battery being charged).
I now tried the second charger, and after awhile of wiggling the radio around in the unit, found a position that held a steady red. Both chargers and two almost identical Baofeng radios are almost brand new, so I would say that it’s just poor design on Baofeng’s part.
So, keep trying to see if you can get the radio to seat in the charger, and good luck!