Clutch push rod will not depress to engage

pull the slave cylinder off and push the piston back in the cylinder then replace all should be ok.

The pressure plate should move when the clutch lever is pulled in if not then ther is something missing or worn not sure on a yamaha but on a honda I think there is a bearing or bushing on the pushrod on the left side of the the tramsmission make sure everything is there look at the parts diagram http://yamahapartshouse.com/oemparts/a/yam/50045a12f8700209bc793c69/clutch

I can't find any parts diagrams for a DT360, and it has been 35 years since I worked on a DT360 at LYNN'S YAMAHA, DM Iowa, but as I recall there IS a ball bearing in the assembly. It went in right before the pushrod. The diagram below is for a 1978 DT400. I am pretty sure your 360 has the same clutch assembly as the 400. The ball bearing would not have worn down. A prior owner leaving it out is far more likely. Please take a moment and rate my answer. Thanks.

You could have put the clutch plate in backwards.

http://www.cmsnl.com/yamaha-yzf-r6mmc-2000_model10891/partslist/

The clutch cable actuates an axle with a gear at the other end. This gear bears against step gears on the thrust rod, which pushes against clutch. Make sure there is a circlip at BOTH ends of this axle. When replacing cover, ensure axle is returned fully with handlever out, and spring is in place on actuating fulcrum of the axle. Thrust rod must bear against roller bearing of the clutch pressure plate. Make sure step gears engage at first tooth when operating handlever. The above link provides an exploded view of the entire bike in appropriate sections as an aid.
Cheers.

I think you mean that the clutch has a broken cable and it is constantly engaged. The clutch dis-engages from the gear box when the clutch lever is pulled in. The push lever axle (I think this is what you are calling the main shaft) sits in a hole on the side cover. The gear on the axle engages the push rod and the push rod separates the clutch plates by pushing on the pressure plate to dis -engage the transmission. If the axle shaft is loose, check the lock bolt. Also check the cover plate. Is the casing cracked or broken at the mounting point?

If you are calling the push rod "the main shaft", then some movement is normal when the clutch is engaged as would happen with a broken cable. Please rate my answer. Thanks.

I would be more concerned with the stuck gear than the clutch, but we will start with the clutch.

The push cam may be bent or deformed and the push shaft may be bent. Assuming the ball bearing is in place, the cam and rod are all that can really go wrong. The rod slides out of the left center case. You will need to loosen the springs to get the left side cover back in place. Roll the rod on a flat surface to see if it is bent. I fear a bent shift fork is causing the gearbox to be stuck in third. Fix the clutch and then post a comment to get back to me.

When you put the sprocket cover back on, you've not engaged the clutch push rod correctly in the clutch slave cylinder. As the cover was tightened down it's pushed the slave cylinder piston too far back.
Remove the slave cylinder only (3 x 8mm head bolts) and check it operates properly, then ensure the push rod is correctly seated in the depression in the centre of the slave cylinder plate when you bolt it back up. FJ1200's have the same clutch and I had the same problem with my FJ...

Here are the possibilities > > Bent clutch push rod, missing push rod ball bearing or push rod, worn out actuator shaft cam, Missing friction disk (5), or pressure plate (4), totally worn out friction disks, clutch plates not installed in the correct sequence, extremely weak clutch springs, stripped teeth on the clutch hub, wrong clutch cable length (inner cable vs outer cable), broken shaft, bent then broken shift fork stems, broken slider gear dogs and a missing shift fork pin.

You didn't say if anyone had worked on the clutch or gearbox so I am throwing in nearly EVERYTHING possible that could create the problem. A little more background and most of the above can be ruled out. Get back to us.