Since it will only run with the choke, it is definentally running lean, backfiring is also a sign of running lean, a lean condition like this is usually caused by an airleak. Don't run it any more then you have to, to find the problem or you could damage the pistons and cylinders. It could be a cracked or loose carb boot,(most likely) A leaking crank seal,(also very likely on a sled of this age) or if it was rebuilt recently the cylinder bolts could be loose and it could suck in air.
Get it running and idling the best you can, and like stormrider said, spray these areas liberally with starting fluid (ether) one at a time. If there is an air leak the engine will most likely rev up, in some cases it will instantly die if it is a very bad leak (witch itdoes sound like)
It could also be the mag side crank seal, witch you cant spray with ether,oilusually leaks past them if they are leaking, you could pop the flywheel off and take a look if you cant find an airleak anywhere else.
If you find no airleaks then it sounds like your pilot jets arepretty clogged.