If it backfired more than likely you have spark.Did you clean the main jet when you had the carb apart. It could be clogged so no or little fuel is getting by. Hence the backfire.
If you have fuel, compression and spark try using a can of starting fluid. If it starts and runs give it a couple more shots of starting fluid. If it continues to run more than likely main jet in carburetor is clogged up.
Replace the carb. They are not that much money and all indications are for whatever reason, their is something defective internally with your current carb.