Also, I do realize that my initial description was vague. The loader starts just fine. The game starts just fine, and I am able to click on the single player button without problem.
Then, I can select an existing world, or create a world, there again without any problem.
The crash happens when actually LOADING a world, in order to play. Usually, it crashes between right after it started displaying things, to after a few to several seconds spent acting (sometimes, I manage to move the view around, sometimes not, but it is utterly impossible to play, as of now.)
Please find enclosed the copy paste of the "Game output (<player_name>)" tab (file named crash.txt).
As you can see, there's been an access violation.
Also, the java version used seems to be a 1.8.0_25-b18, which is strange considering I only have a JDK 1.7 (which I guess has a 1.7 JRE), and a JRE 1.8.0_77, installed (in my C:\Program Files\Java\ directory, they are x64 versions). The 1.8.0_77, I also have in 32 bits.
Any help would be appreciated.
Also, if it makes any difference, the crash was obtained when trying to load a brand new game world, created solely for the purpose of trying to run a game...
Thank you, increasing memory, and disabling VBOs did it.