2005 Durango 4Dr SLT. After inserting the key and turning it, you can hear the car attempting to start for a fraction of a second (that's the sound you hear). If I keep holding the key in the start position, the sound repeats every second or so.

Here's what I have tried so far:
New battery, replaced the starter, reset the immobilizer, made sure key fob has new battery


Please watch the video and advise:

 

bump. Still struggling with this. Going to re-check all the relays and fuses today. If I short the starter, it will crank no problem - so this has to be a wiring/fuse/computer issue. If anyone has been through this, tips would be appreciated.