I need a diagram or schematic of the carb showing the throttle and choke linkages so I can set my linkage for choke and throttle

David, This is what I found in google search for B&S carb. linkage diagram, you can also do a search because there are lots more.
Check the attached links,instruction and guides, Good luck
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The choke linkage is not properly hooked up or adjusted. The throttle linkage is not adjusted properly or there isn't enough vacuum. The choke linkage has a tab that prevents the 4 barrels from opening when the choke is engaged. There is a tab on the throttle linkage from the front 2 barrels that will engage the secondaries when they rotate past a certain point. Vacuum opens the top plates on the secondaries.

The choke linkage moves back and forth left to right.
The throttle linkage is in the center of the carbs and pulls a pulley that turns the throttle butterfly plates.

maybe someone took off the linkage cable what you need here is
to find a schematic of your unit and that should tell you where everything goes on the unit .you should be able to download a
schematic from the web!

YOU dont need a diagram for twin carbys as put them on the manifold back off all throttle linkage and adjustment screws make sure thay are all down, and turn both screws down till they touch, now back off the jets nuts under the carbys and then undo them 2 turns only[thats the ones the choke move up and down] now HB on out of gear a little choke start engine adjust 2 screws 1 more turn each and choke in
make sure you have very thin oil in pistons, then when running adjust jets 1flat at a time when it runs smooth lock up the linkage and adjust screws till idle at 600 RPM.

The problem is more likely that the gas has varnished inside the carb. Mine did the same thing and I cleaned the carb and it ran great afterwards.

Now I have the carb off again because someone dumped a bag of sugar into my gas tank and it got sugar all through the system and into the carb and engine. I couldn't believe how much sugar is in there. Now I'm trying to find a diagram or schematic to show the exact set up for reinstalling the choke and throttle linkage and the spring with the throttle.

Besides the service manual you can view parts diagrams at a dealer like www.arcolawn.com. You can purchase the service manual at a dealer and it will show you how to hook it up.
The throttle linkage hooks up to the throttle shaft closest to the engine. the governor spring attaches the governor arm to the throttle linkage.
The choke cable attaches to the shaft farthest from the engine. I hope this helps.
PS your engine has two factory service bulletins on it.
Joe

It could be several things. It's quite possible that lack of use has made them hard to open. If that's the case then a little penetrating oil and some gentle persuasion will get them working. The top butterflies work on vacuum so you will have to push on them by hand.
It could be that the vacuum pot on the front passenger side of the carb is not working properly.It should connect by a short vacuum line to the top of the carb on the same side. Unplug the hose from one end, stick a finger over it so you don't lose vacuum. There is a long rod off the back of it that goes to the secondary's that should slide when you unhook and hook it back up.
The linkage on the driver's side should move the lower butterflies. Work the throttle linkage by hand, with the car off, and see if they will open. If they don't then liberally spray the linkage with something like WD-40 and work it back and forth. Spray both sides of the carb at the base and in the middle to lubricate the shafts for the butterflies. Work the linkage and spray and it should free up. Make sure that someone hasn't bent the tab that pushes the secondary's open, out of the way.
If the carb has been worked on lately, especially the choke linkage there are lockouts there. If the choke linkage has been taken off and put back on, these lockouts may not be in the right positions. There is a small tab that drops down when the choke is engaged but it can flop around if not correctly installed. You will need a diagram to get the linkage on properly. Most any rebuild kit for that age carb will have a picture of it.
These are your most likely problems. Hope this helps.

SOUND LIKE YOU MISSING THE IDLE SPEED SOLENOID.I REMEMBER I HAD A 81 OLDS 260 V8.IT HAD THE 2 BARREL ROCHESTER.IT HAD THE IDLE SPEED SOLENOID MAKING CONTACT TO THE THROTTLE LEVER.

The easiest thing for you to do is look at another mower that has a single cylinder Briggs at how the linkage is set up. They will all be the same linkage from 12 hp- 20 hp.