Our car is a 5 speed and has the interlock that prevents starting unless the clutch pedal is plugged in. This morning, I went to start the car and just got a clicking sounds that appeared to be coming from the driver's side of the engine.
(New battery installed less than a month ago).

Thinking I didn't have the clutch pedal pushed the whole way in, I let it out, turned the key to start and heard nothing. With the key in the start position, I pushed the clutch in and the clicking sound returned, but the starter did not operate.

A few more cycles of this process and the car started, ran rough for 15 - 30 seconds then was fine. The same thing happened when I went to start the car later in the morning.

Any ideas? Bad starter? Bad interlock switch?