When i tried moving the back bucket on my 2002 580 case backhoe the engine stalled,i restarted the engine but now i have no hydralics,what could be a solution for this problem?

indicates air in the pump
very slow leak to allow pump pressure to drop to a point where it starts but then the supply is below requirement until the continued cranking removes the air and then the engine starts and runs

Can you tell me which injection pump you have on your 580K. It could use a robert bosch or a C.A.V. Let me know I will help you. One thing you need to know, with a cav pump the engine will not have much torque rise in power. The engine is a powerhouse that runs hydraulic pumps at full throttle. This is a full throttle tractor that should run that way all time .If you are trying to back up hill at say half throttle ,it will not do it, try First gear full throttle. Remember the tractor with bucket and backhoe weight is about 16000# . I do not think adjusting the fuel delivery will help this tractor.

most hydraulic hoses on equipment use quick disconnects where the outside section is slid back to release the small balls holding the coupling together
it will be necessary to have the unit in a rest position ( resting on the ground in a neutral position) so that the pressure in the line is reduced to relieve the coupling pressure on the retaining balls and allow the sleeve to move back easily
wash any dirt /mud from the coupling before hand to prevent dirt getting into the system and to make the sleeve movement easier

Pressure valve? does it only do it to only one side? Left or right. The reason you move both tracks with the bucket running is because you relieve pressure. One side is free wheeling, As they call it. I work on cars, But also have done to many hydraulic components. You have a pressure control valve that is bad.

Hi Bill:
I'd check with my local Case dealer. We have several pieces of Case equipment with hydostatic drives.
If I remember correctly, high gear on a standard transmission is a 1:1 ratio in that the power is on a straight through shaft.
My suspicion would be that a shifter link ay have become dis-connected.
Here's a link that may assist.
https://www.google.ca/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=1987+case+backhoe+580k+4x4+transmission+diagram
Cheers

Valves not sealing in the remote control block could be the problem or ram seals.

hydru pump blown or check valve damaged

check hydrallic fluid level in case some of it leaked out. Also check for air in lines by revving it up and trying to engage it under a load. After that, check hydrallic fluid level again.

You're going to have to find the wire that goes to that actuator and put power to it, possibly a bad fuse is causing this. We don't have to remove the bucket very often and this electric cylinder can get bound up with corrosion and pop the fuse. I just removed the electric cylinder from my skid loader that locks my system so I can release it manually. But then I don't know that there is a manual lever on your unit, mines an '86 vintage Toyota skidsteer that I built from 3 I had and rebuilt the 2J diesel engine. It works beautifully. I just love it. My only Case is a '72 Backhoe I rebuilt.