Sorry this is happening to you. Hopefully I can get you started on the road to recovery.
First off, Raspbian is the recommended OS (it's a combination of the words Raspberry and Debian, which is a very common Linux distribution.) It's a good choice if you want the Pi to be as close to "real" Linux as possible. (Yes, I consider Debian to be "real" Linux. No, I'm not interested in arguing about it with any Fedora or Red Hat fans.

)
What do the status lights on your Pi show?
This page should explain what it means.
Most common issues that I've seen which might cause this are:
1) Bad/weak power supply. You had enough power to get into NOOBS but when the installer started doing real work, it needed more than your supply could handle. Make sure you're using a power supply that can source at least 1A (1000 mA)
2) Bad video settings. The Pi might be working fine (status lights will be a hint at this) but it's not speaking to your TV in a way that the TV can display. Could be as simple as a resolution issue, or that it's using HDMI when it should be using composite, or vice versa. Autodetect usually works, but there are settings to force it for this reason. You'll have to give more info before we can troubleshoot this. You could also try a different monitor or TV to see if that helps.
3) Bad SD card. Unlikely, but possible. If this is the case, try reformatting and reinstalling the latest version of NOOBS on it and if it still doesn't work, replace it and install NOOBS again.
You could be seeing something else, but those, in order of most to least likely, are the first things I would check.