Ray,
If you let the machine get up to operating temp with the cap off, and saw no movement in the coolant, then I think you have a few options as to what is going wrong.
First, your friend could be correct in that something has gone wrong with the water pump and it's not pumping. The impellar has corroded perhaps? Does the coolant look brown and rusty, or is it green or reddish orange (depending on the antifreeze used)? Does the coolant look oily?
Next, the radiator could be stopped up internally. If the coolant is nasty, this could be a sign of corrosion which could stop up the radiator internally.
Third, and the place I would probably start, is with the thermostat. If the thermostat is stuck, it will keep the water from circulating and cause the engine to overheat pretty quickly. Should be quicker than 30 minutes, though, if the machine is put to work.
Also, do the gauges on this machine work and are you sure they are accurate?
Remember, I know nothing about your machine and what I am tellilng you are general principles as to how a cooling system works.