Single LED single transistor circuit not working
The base-emitter junction of a bipolar junction transistor is a diode:







simulate this circuit &ndash; Schematic created using CircuitLab

You have another diode in your circuit, the LED. And you obviously understand that you need a current-limiting resistor if you want to connect this diode to a 9V battery, because a diode has an approximately constant voltage drop that is less than your battery voltage.

The problem is the same with the transistor in your circuit. You have the base connected to the positive side of your battery, and the emitter connected to the negative side. You've done this, essentially:







simulate this circuit

What will happen here? A whole lot of current will flow until the battery can supply no more, or something melts. If you are using a 9V battery, it can't supply a whole lot of current, and I bet if you measure the battery voltage in your circuit, it's about 0.65V, unless the battery is dead by now.

So what you need is a current-limiting resistor on the base of the transistor, like this:







simulate this circuit

After you understand that, you might read Why would one drive LEDs with a common emitter?