If you haven't tried a system reset (power off, disconnect the battery from the system board and hold the power button for 30 sec), that's next. If the problem persists, no - there's not "free" fix -- replace the system board.  
Vostro 5590 won't turn on after short circuit. I plug in the power to laptop. The power led turn white and then disappear slowly.   Tried remove the battery, but no help.  any suggestion?
Vostro 5590 won't turn on after short circuit