It's a 3-point plow, right, not a wheel plow?
If it's a 3-point 2x14" plow it should be no sweat for a 4000.
You probably will want your wheel spacing set at 56-60" centers for plowing with that rig.
Yes, it's desirable to use draft control for a 3-pt plow but not absolutely necessary, especially for the first pass.
Try making a pass with the draft control off (position control). Just keep you hand on the position lever and start slow in 1st gear so you can observe. Lower it slowly until it is sinking to where the dirt is just at the top of the moldboard or a little less. Then try taking it up to a proper speed, maybe ~4mph. Use the leveling crank to make both bottoms plow at the same depth; you will have to adjust this for the 2nd pass when the tractor is leaned over from the right side wheel being in the previous furrow. If the tires slip when it is in the ground just 7-8" deep then you need ballast in the rear tires. You should not have to engage differential lock with that tractor/plow combination.
If it works using position control but not with draft control than something is wrong with the tractor 3-pt lift, draft mechanism. or needs an internal adjustment. Of course the top link needs to be proper length, shares in good shape, not rounded points, etc. Coulters can help in pasture but shouldn't cause the problems you're having. If anything, coulters can cause a light weight plow to ride out of the ground in heavy residue. You could try it with the coulters off and then put them back on and adjust properly. You have some moisture in the soil right now, correct, but I hope you're not trying to plow in a soggy field after heavy rains?
