When you installed the LEDs, did you orient them by the flat along one side, or the lengths of the leads? I've had some LEDs where the two orientations differed. The plastic molding was done incorrectly. Try installing new LEDs but don't cut the leads. If they don't work, reverse them and try again. I believe the longer lead is the anode, and the shorter lead is the cathode. Some circuit boards may have a square solder pad and a round solder pad; there should be text that tells you which lead goes into the square or round pad.

You can also measure the voltage across the LED. If it's installed wrong it'll be about one diode drop or near 0.7VDC. If it's installed correctly it will be about 1.8-2.4VDC.

Of course if the driving IC is getting hot I'd replace that first.