What is the wrong with this simple sine wave generator circuit?
The basic problem is that there is no feedback thru the resonating components.  Note that they are tied to the base directly from the power supply.  There is nothing that will make them oscillate.

There are many L-C oscillator circuits out there.  No matter what topology you use, the frequency-setting components either need to be in the feedback path, or somehow arranged to kill the gain at all but the selected frequency.