Sounds like there was almost no coolant left in the engine. That's why the temp gauge didn't work. No coolant in it to heat the sensor/make the gauge work. You must have a leak somewhere. Fill it up with coolant, start it and warm it up. Check for any leaks. Yes the water pump could be bad. Leaking around the input shaft (shaft that sticks out the front of pump and the fan belt pulley bolts on) is not uncommon when a pump gets old. Could be anywhere though. Radiator, hoses, freeze plugs... You might want to change the thermostat too. Could also be the reason there's no coolant. Maybe it got hot and blew all the coolant out? Anyway, hope your engine survived the heat. Good luck.
