2005 durango will not turn over just click even with a boost

Try to tighten the battery terminals, make sure the ground wire has engine/body contact.

Bad connection . Clean battery terminals till they shine .check the battery cable earth clean and tighter .Clean and tighten battery cable to starter motor terminal.

Disconnect the battery and clean both terminals. Wait about 10 minutes before re-connecting battery terminals. That will reset your car's computer. Should start if there is enough juice in the battery. If you hear a clicking sound when you turn on the engine it means your battery is too low to turn the engine and probably means it's time for a new battery. Get someone to give you a boost and it should start fine. Your battery is probably original equipment and more than 8 years old. Thats about maximum life expectancy for a battery.

it may engage but does it freewheel and spin out to high rpm or just turn slowly.. it may be internally shorted.. does the motor turn over by hand with moderate force..

for one, your starter / solonoid unit is in need of attention, even replacement ! it stays engaged, hanging up, solonoid could be going bad, replace the entire unit. check the positive & negative battery cables sometimes they need replaced ! think about it, a cable as big as they are, you would'nt think they would need replaced , but maybe they do ??? just a thought ! alwasy clean battery terminals , put vaseline on them before reconnecting the terminals, it will keep them clean & corrosion free ! clean off battery also, remember its acid, so don't get any on your clothes !

whilst you are trying to jump start it check if you jump leads are good and powerful enough to sent the power to your battery,check if your battery terminals are clean enough to accept the power given,or is your battery not completely dead and even you are boosting has not the power to increase the needing one to start and is just for lights only?

Even a new battery will go dead if the car is running on the battery instead of the alternator.
Check alternator output.
First charge the battery up.
Then check voltage with a meter from Harbor Freight ($3).
Should be 12.5.
The start engine and rev it up.
Should go over 14.
But also clean and grease battery terminals, alternator terminals, and check engine ground strap.

It's possible, they fried your stereo with a flashback.

check, clean  and tighten connections from battery to starter

The battery could be charged... how do the terminal connections on the battery look? Are they clean? Is there signs of corrosion? I would remove the battery terminals and clean them with a battery terminal cleaning brush... even a light coat of corrosion can screw up your electical connection and the "click" can be from not a good solid clean connection.
One trick in a pinch situation I've had success is to take a small sheetrock screw and screw it into the crack between the battery terminal post and the battery connector.... if this improves the situation, then pull the battery terminals and clean them.
Also make sure the battery ground is properly connected at the other end of the ground cable (usually the negative on the batt).

If for some reason your batt is fine, and the starter is just unable to turn the car over due to possible tightness of the motor from sitting, take the spark plugs out and squirt some Dexron type trans fluid in the cylinders... not too much but enough to coat the top of the piston and soak around the rings...
let it soak overnight and then try to turn the engine over with the plugs out... ... let me know what you find... hope this solves your issue. let me know after.
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