Hello Martin_66,
I used to work for Dell support in the past and I know that this can either be an issue with the battery itself, or in some cases with the A/C adapter even if it powers the notebook on properly.
Batteries are considered a consumable item and would have a certain life expectancy as WR2 had indicated.
You can also check out the BIOS, many dell models have a battery health indicator within the bios that give you an idea of where the battery stands.
You can also look in the bios for the status of the AC Adapter itself, if it says "unknown" instead of listing the connected adapter, you will actually need a new AC Adapter even if it powers the unit on successfully.