Given your conditions (a strong rigid container filled with water) it would never boil no matter how much heat you add. The lack of gravity would not change this answer.
Boiling causes water to change from a liquid to a gas. As a liquid, the molecules are always touching (but they are not rigidly connected as they are in ice). So as water they take up little space. In a gas, as steam, the molecules are flying around freely and spend relatively little time bumping into each other. They take up a lot more space as a gas. The pressure of the gas on the walls of a container arises from the constant bombardment of the molecules hitting the walls of the container. If there is less space for the steam then there will be more bumping into the walls so there will be more pressure.
What would happen in your question is that as you add heat the water would try to expand a little. 815
Finding no room for expansion, the pressure would rise dramatically. The boiling point of water is very dependent on the pressure, so as the pressure goes up so does the boiling point.
At some point it will pass the "critical point" of water, beyond which there is no phase change between liquid and gas. The critical point of water is known to be about 374° C and 3212 PSI, which is well over 200 atmospheres.
Now, if you change your conditions to an open container in no gravity, but in a space craft with normal atmospheric pressure, some of the water might gradually float out and form balls because of surface tension. But this is not boiling. It would be hard to heat the water this way.
If you change the conditions again so that the open container is exposed to the vacuum of space, then the vacuum means the boiling point of water pretty much matches the freezing point of water. Water at 20° C would way above the boiling point and so it would instantly (perhaps explosively) boil until the cooling effect of doing so brought the temperature of any remaining water down to near freezing.
At 0.01° C and just under 1% of an atmosphere of pressure, you have reached the triple point of water. This is where ice, liquid water and steam can exist in equilibrium. But in the vacuum of space you have zero pressure and there can be no liquid water. At zero pressure, water sublimes (changes directly from ice to steam with no liquid state, like dry ice) at about -60° C.
Search "critical point of water" and "triple point of water" for more info, Wikipedia articles and YouTube videos. 815