Possible Causes

WARNING: This page is about a different car, the 2003 Toyota Camry. However, it is still accessible from the selected car via links, so may be relevant.

Possible causes are:

DTC P0335

No crankshaft position sensor signal to the ECM during cranking (2 trip detection logic) or no crankshaft position sensor signal to the ECM with engine speed 600 RPM or more (2 trip detection logic).

DTC P0339

If the engine revolution is 1000 RPM or more, the STA signal is OFF and 3 seconds or more has been lapsed after STA signal is switched from ON to OFF, when no crankshaft position sensor (NE) signal is input for 0.05 seconds or more (1 trip detection logic).
Open or short in crankshaft position sensor circuit.
Defective crankshaft position sensor.
Defective crankshaft position sensor plate No. 1.
Defective ECM.