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Some crystal oscillator circuits are using a series capacitor to adjust the crystal load capacitance to an intended value. As far as I see, this is only useful for oscillators with a non-inverting gain block, it won't help in the present circuit.I thought the 10 uF was to block DC, does it have any other applications also ?
The reason why your original circuit doesn't work has already been exhaustively analyzed. It hasn't to do with the series capacitor value. 10 µF is however unreasonably large, the value can be reduced.