I was just playing, I accidentally closed it, then when I open it again, it shows the Mojang sign, goes fullscreen for about 1/10 of a second and then closes.
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Please attach the complete output of the "Development console" which can be found on the second tab of the launcher.
If the launcher closes after game start, please edit your profile and select "Launcher visibility" then, "Keep the launcher open".
Duplicate of MC-14051. Your computer hardware is old, and unlikely able to support game versions higher than 1.7.2. See that report for details.
Change your launcher visibility to "Keep launcher open" and attach development console output.