Test your Petcock,.. don't just turn it to Prime..

If the petcock and fuel system checks out - you could have an electrical problem.  If your bike is not charging properly, it could be losing spark.  The Savage does not have an overabundance of charging ability, and it is known that the spark system needs more voltage than the starter - so you can have a starter that functions and a spark system that does not.

When you say the bike backfires when you let off the starter.....that might mean that when you let go of the starter button the spark system suddenly has enough power to make one spark and ignites the unburned fuel.

Check the fuel system first as Serowbot suggested, then if that checks out check the battery voltage.  With the engine running the battery voltage should read 13-14 volts.  Then check the sidestand safety switch, as it can shut the bike down if the switch or wiring is faulty and the bike is not in neutral.

You have a proper air filter, correct? If it isn't an OEM replacement, you have tuned for the aftermarket filter, right?