Code P340, hard to start?

Sounds like the issue is likely a bad cam sensor. It has to rotate about 10 times so the crankshaft sensor data can be used to create a data point that the ECM can use to get the engine to run. If you have a way to read the live data from the sensor it will show you that it isn't showing a signal. If it is plugged in and the wiring is okay, I would check for voltage and ground and if they are there and it doesn't show any cam sensor data, change out the sensor. Wiring wise the black wire with violet stripe is sensor ground, the Red with green is power with the key on. The brown wire is signal out.
Changing the sensor, you remove the mount on the left side, then remove the bolt and the sensor. Coat the o-ring with oil and install the replacement. The code should clear itself as soon as you try to start it and it sees a good signal.

Ugh, i thought these would be on the back of the engine like newer Minis. I just finished changing the mount on it 2 days ago, i wish i knew. Maybe the wire was damaged from the mount moving the engine as it was in a bad shape.

Could very well be that it got damaged or bumped enough to break the circuit.