Unhook the cable from the carburetor and determine whether it's the cable or the carb that's sticky.  That should cut your monkeying around time by a considerable amount.

Remove the carb & clean it thoroughly, check every crook & nanny. Lancer just posted what to do with a carb so abused.replace the jets & all kinds of things. Look around at other threads & see if you can find it. I cant remember the title.
Congrats! You'll have fun with the bike.

I think if it sat 2 years, the carb needs attention inside, even if the cable is stuck & not the carb. But, Sandy did nail basic T/shooting ideas. Good point Sandy.

AWSOME!! Took me bascially all day. But I completly took apart the carb (cleaned it) and put it back together. I was able to fire it up for the first time ive had it, and probly first time in 2-3 years, if not more. However, about 20 seconds in, i remebered like an idiot, i forgot to check the oil. So i turned it off, and im goin to change it tomorrow, from what i could tell, it didnt have any in it. Hopefully i didnt hurt anything.

THANKS SO MUCH FOR THE HELP!!! And a special think to SavageWahine, I used ur Carb Cleanup post!

idle speed screw is on the left-side of the bike (near the choke and the petc0ck), idle mix is on the right (may be covered with a brass plug).
It's an air-cooled engine and it will get very hot, very fast.  That may be normal.
If you can't make it idle with the idle speed screw, check/replace the spark plug.  Auto parts store $2.00.  Also buy some Seafoam while you're there.  Drain the old gas out of the gas tank, put in fresh with the seafoam added to clean up the goopy old gas residue.

..."put back in suzuki oil"...not the same dirty oil I hope...

If you're sure the tank and carb are clean, then no need for seafoam.  A little marvel mystery oil (no really!), can help clean up deposits and gum in the valves,..say a teaspoon per gallon in the tank.
You might have a gunky build-up on the end of the idle mix screw.  That could cause it to idle bad.  If so you have to drill out the brass plug carefully, it's only about an 1/8" thick and the screw is right under it, remove the idle screw with a small common flat-blade screwdriver (carefull there's a spring behind it) and clean that puppy, spray cleaner down the hole too.
Best of luck,