2005 Pacifica
If the engine has not been run for a few hours or more, when the key is turned there is a "clicking" noise. The vehicle has a new battery, starter and all electrical systems work. It always eventually turns over, sometimes it takes only 3 or 4 tries. Every time you turn the key it clicks fast until eventually, with one of the key turns, the engine turns over. What could it be and what should I do?

 

There are at least two (2) sources of "clicking" noise when one attempts to run the starter. The first click, soft, will be the starter relay in the fuse box under the hood. To verify it, simply swap it out with another identical PN relay in the fuse box. There are several relays with the same PN which are interchangeable.
The second click, more loud, is the click made from the starter solenoid. Yes, I understand you recently replaced this, but some "new" and certainly a lot of the "re-manufactured" starters fail early in the bathtub curve..
To determine which is the culprit will require two people.