Should I replace starter relay , or complete key control switch?

What is your question?

When trying to turn over engine, car will make one click sound then nothing. If I turn key to on position wait about 10 or 15 seconds it will turn over and run. Sometime after driven it will turn over and start right up. Other times it requires the method above.

What makes this problem better or worse?

It doesn't seem to matter what condition of weather.

How long has your 2000 Chrysler 300M had this problem?

few weeks