If you can boot your computer and you have power issues, the best step is to run the internal Dell diagnostics. To get into diagnostics, hit F12 when the Dell splash screens shows, look for the option for diagnostics tests. Generally, it will test everything or you can select which parts to test. For power issues, you want to see that the ac adapter shows up correctly (if it shows up as 1 watt then it is either a bad ac adapter or a bad mother board) and you will want to see if the battery tests as healthy.
If your laptop is still under warranty, you can call Dell tech support and they can help you diagnose the problem and set up repair.