Which LCD board do you use? Reversing the leads doesn't always cause a problem with displays, I've done it several times. On the board somewhere should be a pot to adjust contrast, some of them are very critical because the manufacturer uses too high a value, rather than a lower value and a resistor, or a multi-turn pot. Try adjusting it very slowly. If this doesn't work, you may of course have damaged it, but first check the connectors are really the right way round, sometimes manufacturers diagrams aren't clear or even correct.
