The LED should go on, at least for a while, if this is connected sensibly. I have the following comments:
There is a schematic creator button, please use that to communicate circuits, though the photo is useful in this case too.
You should have series resistor for the LED. The short-circuit output current of the op-amp is enough to possibly damage an LED, but it probably won't happen instantly.
You appear to be trying to stuff stranded wire into a solderless breadboard. Maybe one or more connections are not being made.
The LED may be backwards (usually the long pin would be towards pin 1 of the dual op-amp), or perhaps your battery is dead.
There are some other comments about common mode range of the inputs, however the LM358 will give a proper output if at least one input is within the common-mode range (which is between about 0V and supply voltage minus 2 or 3V). When it is working normally we would expect BOTH inputs to be within that range.
Edit: As per @ChrisStratton, if BOTH inputs are outside the common mode range, then the output will be low and the LED will not light. That is what you have. So you need to bring at least one input within the common mode range.
Edit: Consider the schematic of one of the amplifiers of the LM358:
In your case you have the (+) input tied to V+ through a 10K resistor, so Q3 and Q4 will be "off" and all the 6uA bias current will flow through Q8, meaning the collector of Q9 is almost at ground potential, Q10 drags the base of Q11 down, turning off Q12, the collector is pulled up by the 100uA source and the output rails high.
However if BOTH inputs are close to the V+ supply, the 6uA current source will no longer work and the output will go low. That is your current situation.