I just tried LMNC’s schematics with the first three transistor types I had within reach, and a variety of capacitors, and they all worked just fine (2N3904 and BC547 BC548 oscillated at 14 V, BC337 at 11 V).
It may help to test the circuit with a larger capacitor (e.g. 470 or 1000 uF) since that lets you see if it’s oscillating – the LED will blink or at least pulse. If you go directly to audio, the circuit may simply oscillate outside the (rather limited) range your gear and ears can handle. If you’re outside the audible range, you cannot really tell what it’s doing unless you look at the circuit through an oscilloscope.
Also make sure that you turn the transistor the right way; the voltages above are with the emitter towards plus (note that for the ones I mentioned, 2N3904 has a different pinout than the others), and with the base pin cut off. It may work otherwise, but possibly at other (higher) voltages. EDIT: Tested all three with the emitter towards ground, up to 30 V, and none of them oscillated (not that surprising). They all still worked the other way around after that adventure, though.
Finally, if you switch capacitors, make sure you discharge them before putting them back in, by shorting the pins (*). While they’re not dangerous to you, the components in the circuit may not like having the contents of a fully charged 1000 uF capacitor dumped through them. This also applies if you make other changes, e.g. changing transistors.
*) ideally, you should discharge capacitors through a resistor to minimize the risk that you’ll damage them, but I don’t think it matters much at the levels we’re talking about here.