wow, where to start? First off, you really need to spend a little time reading up on LEDs.
An LED has a specific forward voltage drop - the Vf value from the datasheet. Think of this as the amount of voltage the LED consumes. This can range from 1.7V up to >3V, depending on the LED. Look on the LED datasheet. Most are typically in the 1.9 to 2.1V range. You would think that 1.5V is about 3/4 of that so it should light up. well, no. when you apply the LED with no resistor to the terminals of a 1.5V battery, it effectively creates a short circuit and the voltage will drop significantly. Probably to less than 1V. That's why the LED doesn't light.
However, the LED will be damaged if the current exceeds a device specific limit - If from the datasheet. Typically it's something like 100 mA. There is also a recommended If for continuous operation, probably 20 mA. Since you did nothing to limit the current through the LED, it was probably pretty high - depending on the internal resistance of the battery. If you left it hooked up to the 9V, it would eventually burn out or the battery would overheat and burst open.