I have a 656 International (utility) that spent hours and hours on a 6" hydraulic auger, then a lot of hours on an 8" with hydraulic under-semi pit.  Also had a hydraulic rake and loader, so the whole system got lots of use.

After many years of changing the hydraulic filter faithfully, the whole system shut down, much like you described.  I assumed the pump had quit. 

The local dealer suggested changing the hydraulic oil.  I know we were supposed to change it often, but never in the past had we had a problem, and we assumed those recommendations were made to sell more IH Hi-tran.

It is then we learned that Hy-tran does wear out, especially with heat.

We changed the hydraulic oil, and the tractor still works fine today.

Hope your solution is as simple as ours.  I hate to admit our stupidity, but if it helps someone else, it is worth it.