Friends,
Before I answered, I found the colpitts circuit online and saw that this circuit was missing the two capacitors. I recognized that the base was biased at 1.5 volts which would drive the transistor firmly into saturation and decided that that was probably the reason it wasn't oscillating. Then I entered the OP's circuit into LTSpice and discovered it didn't oscillate either. So I adjusted values of the two resistors until the transistor was biased at about 0.65 volts. The circuit oscillated quite well. Then I added the two capacitors of the internet circuit to his circuit and it would no longer oscillate.
I've had quite a bit of experience with PSPICE and one advantage PSPICE has over LTSpice is that you can set initial conditions for capacitors. SPICE tends to calculate steady state conditions for all components before it starts running and many times oscillators will not oscillate in SPICE when the circuit starts with steady state conditions. Oscillators depend on an imbalance of charge to start oscillating. With PSPICE you do that by setting the initial conditions of the capacitors to 0 V. So when the internet circuit didn't oscillate I looked for a way of setting initial conditions but couldn't find any. Obviously if a circuit doesn't oscillate, though it may be correct, it can't be analyzed. Thus I went back to the OP's original circuit but discovered it would oscillate quite well without the resistors. Note that since with the resistors biasing the transistor at 1.5 V, the circuit with the resistors will always draw more current than one without them. If he hadn't already blown the transistor from his original circuit, removing the resistors wouldn't blow the transistor. If he had already blown the transistor, by eliminating the resistors it will become obvious that the transistor is already blown.
Either way, the circuit I would like to propose to him, still works in LTSpice and yet will reduce the current through the transistor. See attached.
