First of all is the radiator full? If water falls low enough, it will not touch temp sensor, and therefore will give no temp. reading, -- this is very risky, and if it is low enough, it will "boil",-- and push what is left out,. - and warp heads (or worse)!
If radiator full, then it must be thermostat (stuck open), -- which eventeually would read at least some on temp. gauge!problem described (above paragraph),--could be from a bad pressure cap, - which will let water push out possibly enough so doesn't reach temp bulb! Also water will not get as hot with bad pressure cap!
Waterpump is not probelm ,unless water (pump seal) is letting water leak out and getting below temp bulb as described above, -- If not working at all, "Guranteed" it will get very hot very quick!