We have seen multiple Dell N5010 and Dell N5040 laptops recently that will not power up.
This can happen with any kind of laptop. The first thing we check is the AC adapter. If it is providing the correct voltage and current, then we go on to the rest of our checklist.
One common problem is that the power jack (the place the AC adapter plugs into your laptop) can be broken. Big box stores will either tell you to get a new laptop or to replace your entire motherboard. We can actually replace just the power jack itself and your computer will be up and working. We keep most types of power jacks in stock so usually we can repair the laptop the same day you approve the repair.
I am not sure if these Dell models (N5010 and N5040) are any more likely to have their power jack break but I think it is more a situation that these are very popular laptops.