Okay, I don't have 26MHz crystals around, but I got plenty of 20MHz ones, so I used one of these to build a working version of this circuit.
I don't see anything dire about the biasing scheme. It's a bit primitive, but it works for a grounded emitter amplifier: two diode drops mean, more or less, one diode drop for the 33k resistor, and the other diode drop for the transistor. That gives some crude temperature compensation, and a DC current bias of about 0.6/33k = 18uA. That gives (for a beta of 100-200) about 2mA of collector current, as stated in a previous post, and so about 3V of collector voltage. Just for the hell of it, I simulated the biasing with LTSpice from 0 to 100 degrees Celsius, and the biasing is remarkably stable at Ic=2.2mA and Vc=2.7V, agreeing with calculations. I'm not saying that this biasing is ideal, but it has the advantage of directly grounding the emitter which, at VHF and above, is not a bad idea.
The really serious stuff, for me, is the value of the capacitors. Specificly, I think the 100pF cap at the base should be reduced. For about 20 ohms of crystal resistance, the combination of that resistor with the 100pF capacitor gives almost no phase shift at 26MHz. The crystal steps in and provides enough inductive reactance to reach about 80-90 degrees, going quite away from series resonance. Now, the obvious thing to do would be to increase that capacitance quite over 100pF, but then the voltage divider with the reactance of the crystal seems to sink the loop gain beyond what a single transistor can give at that frequency.
So the answer, it seems, is to reduce those 100pF, and let the crystal compensate for the missing reactance. Working at 20MHz, I computed that a 38pF capacitor will force the crystal behave as a 458nH inductor, but the feedback loop will only have an attenuation of 6dB! That is more than enough for the transistor to compensate. Since a 2N3904 has its own 8pF of input capacitance, I settled for a 30pF cap instead of the 100pF of the original.
Here is the circuit (ignore the inductor/variable cap circuit to the right, it's from another experiment). The transistor is a 2N3904, the resistors are the same as in your circuit, the diodes are 1N4148s, but the capacitors are 22pF (as in your circuit) and 30pF (instead of 100pF). In the rear there is a 100nF decoupling cap, like yours. And the crystal is 20MHz, not 26.
The circuit oscillated at the first try. Oscilloscope traces are attached below. My el cheapo oscilloscope is not precise at all with frequency, so the ballpark 20MHz is satisfactory enough. The waveform is far from sinusoidal, but that is not surprising.
So, in brief, my suggestion is: reduce the 100pF to 30pF or so, and try if that oscillates. I don't like this oscillator, the biasing is crude and the oscillation is quite away from series, but it seems to work.