I have a Brigs&Straton 6.5 Quantum lawnmower will not stay running. I can keep it running by restricting the amount of air entering the carb with my finger (choking it) The mower will start if it

Loosen the carb bowl nut until it begins leaking into the shallow clear glass bowl you placed beneath it. It may take a minute to have drained the water out of the bowl and another minute or so to get some more from the gas tank. With the glass bowl you will be able to see the water in the bottom and gas floating on top of it. When you see the gas on top then tighten the bowl nut and try to crank. (Choking helps draw out water still in carb) Return gas collected. to tank but do not let the water go back in.

most newer mower don't us points and haven't in 20years most rough running engines are from dirty carbs

clean the carb

ONLY RUNS WITH CHOKE, IS A FUEL PROBLEM. CHANGED FUEL FILTER. REMOVE THE FUEL LINE FROM CARB. AND SEE IF RUNS OUT.

Try here,you will need the serial number also.

http://www.ereplacementparts.com/murray-lawn-tractor-parts-c-17887_17888.html

After researching the engine application, I see that this 675 is NOT an OHV engine. It appears it is the L (flathead) engine with the standard features. The 775-875 Platinum series mowers have OHV engine applications. That being said, many mowers have the carburetors with the governed throttles set to run at the the OEM mandated maximum speed. Some (like the Briggs Quantum series engines) have the throttle plate still attatched. You would need to bend it back up and install an aftermarket throttle cable assembley (like Murray makes). You would connect the carburetor end of the throttle cable to the hole in the plate assembly that has the governor spring attatched. Some even remove the governor entirely (internal governor has to stay in) and connect a throttle cable on the plate controlling the butterfly in the carb. Your unit may have this feature with the plate having a few different holes in it in which you could install the end of an add on throttle cable.

it sounds like a fuel problem.
first drian fuel out of tank.
i know you have already cleaned the carby but dis assemble carby and clean with carby cleaner.
re assemble carby & fill tank with fresh fuel.
also clean air filter & check oil level & check spark plug,if the spark plug is black and the tip is blocked with oil build up, then replace.

The solenoid on carb was bad causing reduced gas to motor and low power

The jets in carbs are really small and clog easily. If you stored your mower with gas in it start by replacing the gas. Remove the air filter and prime the carb. Start the engine and place your fingers over the air intake on the carb. This will cause the engine to stall as it will be starved for air. It will also create a powerful suction on the jets and possibly dislodge a blockage. Prime the engine again and start. If does not continue to run, repeat the steps again. If after 3-4 tries your engine wont run you will have to remove the carb and clean the jets manually. The reason your engine runs for a short time is because it is burning the fuel that you put in there by priming it. After that the fuel comes through the jets in the carb and if these jets are clogged the engine will die.

high jet is clogged up need to clean carb from inside