Backfire car wont start

If you got a backfire, the timing is off.

Cars haven't had carburetors since 1985 some 29 years

To backfire thru the intake, you can't use the car,has to be
a timing or valve problem,probably a mechanical failure

These seem to be unrelated, did the car backfire violently before this happened? The timing chain may have jumped cause a mechanical backfire that cracked your oil filter. This very hard to diagnose, can you give more info, does the car seem to turn over normally.

Well technically you have fuel in the engine if you are getting a backfire in the intake. I would say the fuel is getting thru the injectors.
But maybe not at the right time.
Has anything happened to the timing belt or cams ?

backfire out exhaust or intake?

if it is backfirering sound like timing is out of spects

Engine system needs inspection on case of backfire:-----

Check out related help links to troubleshoot the vehicle backfire issues:-----

Feels like backfire from engine when decelerating?

http://schematicsdiagram.blogspot.in/2012/02/feels-like-backfire-from-engine-when.html

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Jeep Backfires?

http://technoanswers.blogspot.in/2012/02/jeep-backfires.html

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Nissan Pathfinder stalls and bucks on Acceleration?

http://technoanswers.blogspot.in/2012/02/nissan-pathfinder-stalls-and-bucks-on.html

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Nissan Pathfinder Backfires?

http://technoanswers.blogspot.in/2012/02/nissan-pathfinder-backfires.html
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These will help.
Thanks.

Sounds like an ignition or timing problem.
Is the check engine light on ?
This engine uses a direct ignition system which means each cylinder has a coil on top of the spark plug. It could be as simple as worn out spark plugs.
If you had said the engine backfired and was hard to start, but no flooding, I would also look at low fuel pressure. But too much fuel causes flooding.
A faulty throttle position sensor could cause all of your symptoms, but it should set a trouble code and turn on the check engine light.

Don't know what caused the backfire, but often the pressure from the backfire causes a vacuum line to come off (usually a large one; brake booster, PCV or similar size). this lets extra air past the throttle butterfly and raises the idle speed. find your vacuum leak and the idle speed should return to normal.

sounds like you have jumped a tooth on the timing if not timing out