C19 at 10MHz give a reactance of .0159Ohms, which is a short essentially (thought that was purpose of that cap?).
I've realized that C19's value is not that vital an issue. Your original value should permit the project to work.
It's true that a larger cap value creates more phase change than a smaller value, but this probably makes no big difference.
Forgot to mention my bias current Ic=1mA
The resistor network I made based on the fact that the base voltage is 1.5V (from R4 drop) + .7 (forward bias diode drop base to emitter) = 2.2V. I've heard that the rule of thumb for picking (to neglect the base current) R3 is R3<10*R4-----> R3<15K so I picked R3 to be 7k. From that the current going through the bias branch is then 2.2V/7Kohm=314uA. Based on the approximation that the base current is approximately zero; I solved for R1 from (12V-2.2V)/R1=314uA, R1=31K. I thought all those approximations were the right way to bias the bjt?
Consider raising the bias to 2 or 3mA. If you're lucky you'll get a couple mA flowing around the control network. This would turn off the transistor some of the time if you were to keep a 1mA bias current.
When working with a real circuit it is very convenient to hook up a potentiometer between the supply rails. Tap off the center terminal to supply the bias current. Then you would dial around til you find the proper position that creates oscillations. Or if not oscillations, then a few ringing waveforms which decay. It would let you see if you're close to success.
With a real circuit you sometimes have to administer a 'shock' to get things going. This might mean discharging a capacitor, disconnecting and reconnecting power, attaching a resistor somewhere momentarily. Etc.
So are we talking like 1ohm or so for the resistance in the inductor?
A real coil will have more than 20 ohms. Most of the time we don't necessarily want much resistance in the coil, but it could help during troubleshooting if we ensure that some current is diverted to the capacitors. It's a tactic to see if we can reduce the tendency of the oscillator to 'stagnate' at power-up.
Would the DC blocking cap at the top of the LC network just go to ground? But wouldn't that effect the resonant freq?
Your configuration may not need an additional cap, since you have caps at all the other avenues.
The bias current is only 1mA, so maybe bias for a bit more
See my answer a few lines up.
The falstad.com website has this animated simulation of a Colpitts. Although it is greatly simplified, it illustrates the action you're wanting to generate in the LC control network.
Colpitts Oscillator
It does not show the trouble encountered trying to get it to start oscillating.
It has no constant bias current to the transistor. (Your bias will shift the waveform higher to become a sine wave.)
It lacks the DC-blocking capacitor which you have.
It uses lower resistor values.
It has a lower supply voltage. Testing various supply voltages may be worth a try in your circuit.