First - I wanted to thank all of the members here for providing a robust and well-documented forum for these S40/Savage motorcycles.  I had no idea where to start and stumbled across this forum and have spent HOURS reading everything out there.  

Back story -- I had a Canadian buddy that bought a 2007 S40 and never rode it again after 2008.  It had been sitting in the garage since (14 years) with the original oil and same gas in it.  I was given the bike for free as a project with my kids to get it running and have some fun.

So far I've replaced the oil, spark plug, air filter, battery -- and I was into the bike for about $100.  Then I started the bike and it just simply WAS NOT  happy.  I also noticed some fuel leaking from the petcock area and instantly purchased an OEM Raptor 660 petcock (thanks to all of the suggestions here).

I pulled off the carb and after removing the bowl... found the main jet in the bottom of the bowl broken off.  It had corroded and the build up in there was nothing like I've ever seen in a carb before.  BLACK GUNK caked everywhere.  Anyway - I ordered one of those eBay carb rebuild kits immediately (before seeing DBM's write up on the kits   ) and started to take apart the carb.  Here's where I'm at now...

- The float is virtually stuck.  I've tried almost everything to remove that hinge pin, but I'm fairly certain any more is going to break something permanently.
- I have no way of removing that main jet without the screw head available to me that I'm aware of

Before I start looking to buy pieces one at a time and replacing everything slowly -- am I better off just buying a brand new $600 carb and being done with this entire piece-by-piece approach?  The bike has virtually no mileage on it...

Thanks for the suggestions and I look forward to getting this motorcycle to run.  I think I want to do the Blue Collar Bobber route -- but not sure yet since I don't fit on the bike anyway (I'm 6'5" on this small bike)...

If just soaking doesn't get it, it really looks like a ultrasonic cleaning candidate.
That is crusty looking.

I think you're moving pretty fast. Slow down and think before tossing money.
You ditched a virtually new plug. How much dirt fell in the cylinder when it came out? The fewer things touched the less likely something will go wrong. Go straight for getting it running.

It sat how long? Before the piston goes raking the cylinder walls, maybe shoot some oil in it?
I use a torch cleaning set for jet cleaning. I'd soak the crap out of it first, and IDK if it's okay to soak the rubber bits.

If you aren't successful in getting your carb to work.....and you want a stock carb.

Here is one that is completely rebuilt and ready to go for $350.

http://suzukisavage.com/cgi-bin/YaBB.pl?num=1399394334/0#7

It's repairable, sure, but if I could get a known good one for forty bucks, I'd probably jump on that. I'd still take a swing at fixing that one, but I'd start with making the bike run.
I'd get oil in the jug, and spin it over with the plug out.
After cleaning up where the plug sits down in the hole.
I didn't. And figured it out before the new one went in. Went Fishing with a piece of weed eater string with some toilet bowl wax and retrieved a Coupla chunks of road crap. That is why I'm always harping on that.
I'd be wanting to prove it's wanting to run.
A shot of ether, brake cleaner, or WD40 ,and I don't much like WD, but it's a good option here. It's a short term lubricant, shoot it in the plug hole, roll the bike in gear, spread it around, then spin it with the starter to avoid oiling the plug, stick the plug in, and if you have an old spark plug wire to steal the end that sticks on the plug, it makes a great way to start a plug. A dab of anti seize is something I choose,
Then a quick squirt in the intake and hit the starter and just see if it Coffs,,
If not, hit it again, harder.
IDK if WD is still using propane for a propellant. Maybe shooting some over a lighter and see if you get a flame thrower.
Full disclosure
Lighter must be lit. Situational Awareness is required.

Then when you get a carburetor on, if it doesn't at least Coff,, it's the carburetor..

Well, fuel delivery,,

The fuel is Allowed to flow to the carburetor when vacuum opens the petcock. It's Old and stiff. And it won't fill the bowl unless you set it to Prime. So you can run the starter ragged and suck the battery down and it's still spinning but it's Not hot enough to make it fire the plug.
Be prepared to shoot something into it to get it trying to start, it saves wear and tear on starters and batteries And it gives you feedback.
I hope you saved your air filter. It's basically new. Needs a puff of air,
What plug did you install?
If it doesn't want to run,remember, it was running when the other plug was in there.
Doubtful you bought a New plug that was JunkInABox,,but that would sure create confusion.