The laptop may be one of those Dell's that were designed to work correctly only with the proper original/replacement genuine-Dell adapter. I've never run across one (I've used a universal adapter/charger with quite a few Dells), but I've run into repair folks that say they have and I've read some documentation on it. The way I understand it, it's not a separate wire but rather a signal generated by the adapter that's superimposed onto the power line to the laptop. I'm not sure if all the Dells that were built this way behave the same way when using a non-genuine adapter; a behavior I recall is that the machine will run on the adapter but the battery will not charge.
If you go into the one time boot menu during a restart attempt (F10 or F12 I think) you may find an entry that'll run diagnostics on the machine. If so, you may find that it'll automatically run through some tests and then at the end it'll let you run selected tests, a few of which may be related directly to power/battery/adapter.