Welcome. Those console warnings, we need them. Click on the 'Paste my log to pastebin.com' button. This will add a link, pastebin.com/xxxxx, at the bottom. Type or paste that link here so we can see your log.
You did not say the console closes, just that the game crashes. A lot of times the game crashes but the console stays open. See if there is a crash log in the launcher folder. If there is please post the information (text) from that file to pastebin.com and provide the link that pastebin gives. Thanks.
Here is the log http://pastebin.com/TbufCjH2
Why is your allocation of RAM at 512MB? Your computer is 32bit which means you can go up to 1GB and that will help, but might not fix the out of memory error you are having.I am having a problem like this. I load the launcher and try to create a new world but it will crash before I can get in game.
Log: http://pastebin.com/tPSaGupf