My 660 grizzly was working fine when i stored it last fall, but over the winter the battery went down and i lost the keys to the inigtion,so i dissconnected the ingition wires joined them all together and boosted it with my truck it turns over like crazy ,spray gas in the carb and it run for few seconds then dies lots of gas going to carb dont know if the ingition has some kind of fuel safety in it or the carb needs to be cleaned. also i had it stuck in the mud before i but it away for the winter...

SOURCE: 2007 Yamaha grizzly 660 wll run fine, and then

CHECK VALVE CLEARANCES(INTAKES MOSTY) IS IT ONLY HARD TO START AFTER IT HAS BEEN RUNNING(HOT) OR IS IT HARD TO START COLD TOO?

SOURCE: Won't idle without choke

The pilot jet controls the air/gas fuel mix at idle . If the jet gets plugged up not enough gas gets to the emgine at idle. You will need to remove the carbs and float bowls and clean them, paying special attention to the pilot valve. Count the number of turns to remove the pilot screw and replace the same number of turns then turn counter clockwise 1/2 turn.

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SOURCE: yamaha 125 grizzly starts and idles when choked but dies when acc

Take the carburetor apart again, remove the main and idle jets and idle mix screw, plus the float and needle valve. The main jet holds an 'emulsion tube' in--look inside where the slide valve moves, you should see a short brass tube projecting out of the bottom. Carefully push down on that tube with a plastic rod or wooden dowel, it should drop out the hole where the main jet was. Chances are that the tube is dirty and needs to be cleaned--look carefully at the series of small holes drilled into the sides of the tube. These small holes deliver air which is mixed into the fuel passed through the main jet. That air comes from a small hole just inside the intake side of the carburetor. The long needle that sticks out of the slide bottom controls low to mid-range speed fuel-mixture. Check that the 'C' clip on the top end of the needle is in the center groove and that the retainer spring is pressed down the 'C' clip. Now soak the whole carburetor with spray cleaner, then blow out all passages with compressed air. Don't soak the rubber-tipped needle valve from under the float. On reassembly, set the idle mix screw 1-1/2 to 2 turns CCW from CW stop. Adjust for best idle after you get it running and warmed up. I hope this long winded explanation helps!

SOURCE: 2005 grizzly 660 rear drive shafts pop out of the gear box a lot

There should be a circlips at the end of the driveshaft.
That circlips holds the shaft IN the differential parts.

If you have still warranty, let it repair by a dealer. The circlips is maybe INSIDE the differential casing and can thus destroy a lot of parts!