I used to have a similar problem with my Kaide world band radio. Once I
connected the AC adaptor plug to it, it stopped working even when
there was battery inside. LCD display went blank, too.

Turned out the cause of the problem was that the plug didn't perfectly
fit the socket on the radio although it appeared to fit. I twisted the
plug and pull it out a bit. The radio then worked intermittently. It
therefore was a problem of poor contact.

I then used another plug that finally proved to fit perfectly. No more
problem.