Why isn't this astable multivibrator oscillating?
The diodes are the problem. As modified, the circuit has a stable state, with both transistors turned on, and about 0.7 volts on both sides of both capacitors.

Consider that the circuit was turned off for "long enough" for the caps to discharge to zero. When you apply power, the caps start out at zero, and R2, R3, R4, and R5 all follow the power rail as it starts to go up. When the transistor bases get up to about 0.7 Volts, the transistors turn on with the current through those resistors. That clamps the collectors near zero. The anodes of the diodes can get pulled up to 0.7 above the transistor collectors, and that's enough to turn on the transistor bases.

You could replace your 1N4007 diodes with lower-voltage Schottkey diodes (maybe a BAT48, or 1N5817, 18, or 19), and that might allow the circuit to oscillate, but I'm not sure you'd really achieve your goal.

Here's a selection of likely Schottky diodes at Digikey: http://tinyurl.com/qat53yk