The Java Runtime Environment is usually pretty safe to download and use on your computer, especially if you downloaded it from the official Oracle or Java website.
Perhaps there was some other factor or factors that caused your computer to not work properly after you downloaded the JRE the first time you did so, as it shouldn't cause problems, especially like the ones you described, when downloaded and installed.
If you'd like to download the Java Runtime Environment again, so that you can play MineCraft and use other applications and games that require the JRE, you can do so from the link below.
http://java.com/en/download/index.jsp
However, if you're worried that something may go wrong with your computer or that you may lose all of your files and programs upon downloading and installing Java, I would suggest that you back-up all of the data that you would like to save, in the event something does go wrong.
Good luck and I hope I helped you!