Howdy,
Do you have a URL for the crystal specification? I'll look for my gate oscillator spreadsheet and drop the values into it.
Have you tried more than one crystal?
Remember that the gate should be biased into the linear operating range to get things started. Sometimes a small resistance in series with the gate output is necessary in addition to the 10M-20M feedback resistor.
Then the pi section (the two caps and the crystal) provides
180 degrees of phase shift, which when added 180 degrees from the inverting gate satisfies the 360 degree round the loop requirement. The other requirement is loop gain greater than unity, but the gate has more than enough gain to compensate for the loss across the pi network.
With low frequency crystals (~100KHz and below) the gate oscillator usually works, so this is a puzzle. If you have a 4049 inverter I'd try that. They make vigorous LF oscillators. With the 4049 use 10M feedback 49pf and 56pf on either side of the crystal (highest value on the gate's output side) Also use
39pF between the gate output and the pi section (where some application notes show a few K-Ohms of resistance.) Of course the
10M bias resistor must be directly connected from input to output of the gate to force it into linear operation.
I have a pierce circuit with an inductor insted of a resistor in the drain(2.5mH because it's what was handy.) Every LF crystal or ceramic resonator that I've tried, mostly salvaged from computer junk, has oscillated if it was ever going to oscillate. I don't like the app note oscillator for LF crystals. The pi section capacitors and feedback resistor are too low in value and the drain resistor would be better replaced by an inductor. But I can't say it wouldn't work.
Don't be too hard on cut and try (trial and error) somtimes a person stumbles onto something wonderful via that path.