If the power supply you are using tests ok, and that the jack on the side of the radio isn't broken, it is likely something more serious. I have repaired a 250d with the exact symptoms. It is difficult to diagnose problems like this without the radio in hand, however have you ever accidentally somehow connected the battery backwards? Doing so will result in the exact problem that you are describing. When the battery is connected backwards, a zener diode in the charging circuit will fail. The radio will still power using the battery pack, but will not run off of the power supply, and the batteries must be charged externally.
If you are capable of some simple component level troubleshooting, I have attached a picture showing the location of the diode. Keep in mind that these are surface mount components, and can be difficult to repair if you've never done this type of work before. In the attached photo, the white powder next to "LND4" is the diode to look for.
There could be other problems as well, but this is just what I have seen in the past. So I'm passing it along.
Good luck
-Jim