You've got a number of possibilities to check. The tracks and blade are both operated through the swivel joint. You can look it up in your manual. Basically, it's the thing that let's fluid get to all of the operating gear below the house, so that you can swing continuously without wrapping up a bunch of hoses. If it leaks to another section, you won't see any evidence of oil leakage externally, but you won't deliver flow at pressure to your intended system.
If pushing tries to stall the engine, you may have fuel delivery problems in the engine itself and not a hydraulic problem. If you push against an immovable object, it should either spin the tracks, or open the track relief valve. It should not stall the engine.
Look in your manual for the procedure to test leak by in the swivel and see if that's something you feel comfortable with. Otherwise, you may have to find a "traveling" professional.
Greg