Post the rest of the specs of the machine if handy, or the model if you have it.
As far as the GPU, you're in a bit of a pinch because those older GTX models aren't supported by more recent drivers. Looking at the docs, it IS supported up to the 470 release, which means any distro would be fine as long you make sure to install and pin that 470 version of the drivers if you want to game.
If you don't want to do any heavy gaming, then any distro will work with the Nouveau drivers, and should be detected automatically out of the box.
As far as the not booting....I would expect the display just not to start properly, but the machine is actually booting. Many ways you can confirm this if needed.