I had a similar issue on my 300 that I just bought, and this thread came up when i was searching for a solution. I also have a repair manual, which proved extremely helpful when diagnosing my particular problem. I would like to post a background of how this system works and a basic way of testing it for those that do not have a manual.
The symptoms were identical on my machine to those described here, the only caveat is that my tractor has a 3 point hitch and no backhoe.
The 300 industrial has 2 hydraulic pumps. One pump is inside the transmission, the second is mounted in front of the engine, driven by a coupler. The pump ahead of the engine is a closed center, constant pressure pump. Oil to this pump is supplied by the pump in the transmission, which also runs the reverser (in my case the power steering), power brakes, and lastly, lubricates the transmission.
To test the transmission pump:
There is a right angle rubber hose running from a reservoir above the front pump, and into a cooler connected to the radiator. That hose is a bypass for all oil that isn't used by any of the other functions that are run by the transmission pump. If you take that off, oil should come out at a rate of 1 gallon every 10 seconds. When I took that hose off mine, it was completely dry.
Then, I had to determine where the oil was going. There are 3 test ports on the power reverser. One on the back of the housing (all take 1/2" sockets, and the plugs are 5/16" fine thread bolts I think), and 2 on the top of the housing when you take off the right footrest. Test the pressure at each of these ports. It should be 150 psi or so at the back port, and the same at the other two when shifted in forward or reverse (one plug is the forward clutch test port, the other is the reverse clutch test port). Mine checked out fine. This told me that the transmission pump is fine and was building pressure.
There is also a small possibility that a filter bypass is plugged inside the reverser housing. to check, pull the housing off the back of the reverser (6 socket cap screws) The valves inside and the springs were all clean on mine.
On the original posters issue-if he had done this test, his forward and reverse clutch pressure readings would have been very low. If they are low, the pressure regulator will not allow oil to leave the reverser until pressure is where it should be, which starves everything else of oil. This is my understanding at least. Mine checked out fine, so I will continue.
The last possibility is that one of the high pressure hydraulic systems was leaking internally, using all the oil. The transmission pump is only about 6 gallons per minute, and the main pump is 20+. If the oil is being used internally and not sent back to the main pump, the pump will run out of oil (which is why I was getting no flow out of the hose connecting the reservoir to the oil cooler). To test this, cap off each hydraulic function one at a time. (I used a hose with a high pressure gage on the other end. This allowed me to cap, and watch oil pressure all at the same time). In the end, it appears that my 3 point hitch is leakign internally, either in the cylinder or the valving. The hitch functions correctly, except when the oil pressure drops-there was no indication at all that there was a problem except for this test. With the 3 point hitch inlet capped, and only the bucket in the high pressure system at this point, it functions exactly as it's supposed to.
So in the end, it was the 3 point hitch.
I hope this description is helpful to someone experiencing this issue down the road. Like I said, it is the first thing that appears in google when searching this issue, so I figure I'd add my experiences to hopefully save someone else some headache.