But when I minimize it, the program closes, and won't open again. What is happening?
Bitcoin-qt might minimize to system tray. Does it say "Cannot obtain lock on data directory ... ... Bitcoin is probably already running." when you attempt to open it again?
Well, in that case bitcoin is already running, like it says. All you have to do is open it from your system tray, which is located at bottom right of your screen should you be using a Windows OS of some sorts.