Problem 1) have you cleaned the carb? your jets may be plugged.How long was the bike not running/how may miles on it ?What year is it?
problem 2) the leak, you need to give more info ,is it a cap nut under the center bottom of the head ? or is the leak on top under the chrome cover? or is it coming from the area near the exhaust header?
 We can't see the leak from here!

http://suzukisavage.com/cgi-bin/YaBB.pl?num=1099227295

One of our resident carb gurus can chine in with specifics, but I also agree that it sounds like a carb that just needs a good cleaning. You have no idea what the previous owner did before they put it away, and most likely gunk has settled in the jets.

I suggest a thorough carb cleaning with special attention to the jets.

Also make certain that the diaphragm slide and carb body where it slides in are cleaned well (NOT with carb cleaner...you don't want that on any plastic or rubber parts) with maybe WD40 and the slide is wiped clean with a lint free cloth and put back into the carb with NO greasy fingerprints on the slide or carb body.  Fingerprints will attract dirt and result in a sticky slide and throttle issues.

Hope this helps!

Sounds like your float got stuck and fuel dumped out of the overflow
I recommend checking your oil for fuel, usually doesn't happen but it can,

Take your carb apart and clean your jets or better yet, swap out your jets while you're in there.
The bike comes jetted lean from the factory with I think 47.5 pilot and 145 main jet
Depending on your location a 50 pilot and 150 main jet works for ppl with a stock or dyna muffler, i like 52.5 and 152.5 in the New york area

Alrighty quick update.
Come to find out when I took the carb apart the diaphragm was missing parts (go figure) the last owner must have took it apart and didn't put everything back. So I have to order a rebuild kit and I get back to update you again.

Hey everyone,

So I my bike to start without the coke being open.  My next problem is that I can not give it any throttle with out the bike dieing on me.
The carb is rebuilt.
Fresh gas.  
The petcock filters are clean.

Not sure why it dies when I give it throttle.

Exactly what did you do in cleaning the carb? did you clean : all the passages ,jets , the tiny filter in the carb just above the float valve seat, did you inspect the float valve for wear, did you check the O-ring on the outside of the float valve seat, did you set the float height , did you place the washer on the main jet before screwing it in? did you change jet sizes / exhaust ?  We need more info. The bike dies because it's either getting to much fuel or to little when you open the throttle.