Cont test everything. One bad joint and you're now looking at a completely different circuit than what's in the schematic. Make sure everything that's connected should be, and also make sure that you haven't inadvertently connected anything that shouldn't be (for example, adjacent IC terminals).
Next, print out a copy of the schematic, pick a reference point (the negative battery terminal should be good), then start measuring all node voltages with respect to that point and recording it on the schematic. Pay special attention to the IC terminals (it wouldn't be the first time someone let the magic smoke out). Double check that all of the values are sane. (You need a function generator and preferably an oscilloscope to be thorough here, but a DC check is a start.)
That LED you got backwards isn't the only thing in the circuit with a polarity, and you already got one thing reversed. Check that everything is the right way around. Including the ICs.
Edited by gimble - 9/5/10 at 1:27am