Fix black screen with following steps:
You can "reset" them by unplugging it, removing the battery, then the RAM, replace the RAM then the battery. This can clear all kinds of minor glitches. However, if the problem is of a more serious nature then you may have to contemplate cutting your losses and getting a new laptop as this one is worth less than it would cost to have it repaired professionally.
Check Dell Latitude E6410 Manual for more support.