Here is a hypothetical hydraulic problem and how to trouble shoot it.

"We have a hydraulic system that operates two cylinders. The pump (piston-type) has failed - for reasons unknown at this time. The tank, valves and cylinders were cleaned and a replacement pump installed. The new pump is delivering a maximum pressure of 1,000 PSI and appears to be creating heat."

In any troubleshooting situation, no matter how simple or complex the hydraulic system, always start with the basics. This ensures that the obvious is never overlooked. In order for the 'obvious' to be obvious, the fundamental laws of hydraulics must be kept in mind:

• Hydraulic pumps create flow - not pressure.
• Resistance to flow creates pressure.
• Flow determines actuator speed.
• Pressure determines actuator force.
• Fluid under pressure takes the path of least resistance.
• When fluid moves from an area of high pressure to an area of low pressure (pressure drop) without performing useful work, heat is generated.

Theory is great, but it always makes more sense when put into practice. So let's apply these fundamentals to the above situation in a way that ensures the obvious things are not overlooked.  

"The new pump is delivering a maximum pressure of 1,000 PSI..."

We know that a hydraulic pump can only produce flow (pressure is created by resistance to flow). It follows that if the pump can't get oil it can't produce flow. So, check that the reservoir is filled to the correct level, the breather is not clogged, the suction strainer or filter (if fitted) is not clogged, the pump intake isolation valve is fully open, and the pump intake line is otherwise unrestricted.  

If the pump is producing flow, then an absence of pressure indicates an absence of resistance to flow. Knowing this, and that fluid under pressure always takes the path of least resistance, the task now is to find the point at which pump flow is escaping from the circuit. If you're skilled in reading and interpreting hydraulic symbols, the system's schematic diagram (if available) can be useful in identifying possible locations.

"The new pump... appears to be creating heat."

Because heat is generated when there is a pressure drop, using an infrared thermometer to check the temperature of individual components will quickly lead us to the hottest part of the system - and the probable location of the internal leakage. Note that in a properly functioning system fitted with a piston pump, it is not unusual for the pump case to be the hottest part of the circuit.  

The above checks should have taken less than 10 minutes. If nothing conclusive was revealed, I would continue the process of elimination using a flow-tester to conduct a direct pump test.