I have this issue that can be frustrating.

Sometimes the ignition switch is just dead. The car will be running fine. I stop to get gas and try to start and turn key and nothing. Panel lights come on but switch is dead. 5 minutes later, 10 minutes later, the car starts as normal.

Also, in cold weather, when you turn the key for the first start, the car continues to turn over for about 5 seconds. It only happens on the first turn.

I have replaced starter. Is this a ignition cable issue?

 

Are you stating In cold weather the engine turns over for 5 seconds after you release the ign key?

Does the car have a manual or automatic transmission?

For a manual transmission the starters electrical system has a starter relay (which is in addition to the starter solenoid) wired into the clutch pedal safety switch. If this starter relay is stuck closed or ign switch contacts sticking the starter can keep cranking once key is released.

For automatic trans the trans has a park/neutral switch that prevents starting unless trans is in Park or Neutral. There is not additional starter relay here.

When the key is turned to start but there is no starter response jump the starter solenoid (small wire on solenoid) with 12v. If the engine now cranks the issue is the starter circuit. Make sure trans is out of gear or in neutral/park and emergency brake on.

The ign key "switch" is actually several switches gained together. Thus one switch can operate OK and another have problems.