That's a good sign.
Check under the dash for a chip-type anti-theft system... one where you can take the "key" with you or an odd aftermarket receiver you've never understood what it was for. Dealers sometimes install these things up front, then try to sell the anti-theft system after the fact. If not bought, there will be a blocker chip placed in the receiver, something that may have finally worn out.
It'll be placed in a conspicuous spot, near the bottom of the driver's side dash.
Here's the starter circuit. You've got only two fuses to check underhood and then we'll take a look at the starter relay control circuit, which comes from the transmission controller.
If you have a voltmeter or test light handy, you'll have a few things to check. Remove the starter relay and look at the base of the relay for pin positions... transpose them to the fuse/ relay block for location.
The only HOT terminal all the time will be Pin 30, which is a direct battery feed through Fuse 9, a red cartridge-type fuse in the same box. This circuit supplies the output voltage to the starter solenoid through the relay.
Your key switch will send 12v to terminal 86 when turned to the crank position, the only time you'll see power there.
The all-important ground circuit on the control side of the relay (supplied by trans controller) is Pin 85. If you reverse the polarity of the test light clip from negative to positive and probe Pin 85, it should light as you place the transmission in either park or neutral.
Finally, output is on Pin 87 of the relay and sends power along a brown wire to the starter. Check to see if the wire is getting powered by the relay when the switch is turned.
At that point, it's all up to the connection at the starter and the starter itself.
Check a few of those things and let me know what you find. This is an unusual problem on the Durango...
Talk in a few!