XOR with 3 different OR gates
As Tom pointed out, the problem is that you've shorted the inputs together, so that either A or B active means that the gate will be off, same as if they were both high. Also, you should have a series resistor for the LED. Below is a fix for the immediate problem, also showing \$\text R_{LED}\$, the series LED resistor. 



You could also add two diodes rather than the transistor to isolate the inputs from each other.