As I asked before have you tried running the default game or something like Hoopah's LA mod (unaltered) to see if it still crashes after a specific duration. Your comp has an integrated chipset (amd). I had a similar chipset on one of my laptops and it ran the game, albeit lighting was prone to causing lag. Until you have either tried the default game and/or LA mod or similar low-demand spec mod I cannot speak further for your situation.
Looking @ your DX diag your machine has a total of 6 gigs ram, of which roughly 5.6 is available for the os to start with, your video card "dedicated" memory is the missing portion of the 6 gigs... Your OS will consume around 1 gig it's self just for the normal operation of the system at a minimum. Leaving around 4.6 gigs +/- for programs/operations.. But realize your video card has the ability to consume more of the physical memory if it is similar to the AMD chipset I had previously, so it is possible it is consuming more memory for the video card than the "dedicated" 500 mb or so it takes off the bat.
Whatever is left after that, would be around (ballparking) 3 gigs can go to the video card, 1 gig for the system run, leaving 2 gigs for the game and other applications to run on if the video card chews all that it can. Make sure that when trying to play the game you shut down any anti-viruses you have running on your machine, some of them will try to check the game as it runs (because it runs scripts) and that can cause excessive resource consumption. But ultimately, the computer is not ideal for gaming, so try the things I've suggested above before I can even consider any other alternatives you may try. Obviously, make sure the computer is set to "high performance" for it's power setting and not power saver or balanced as they will reduce the available power to the machine.
Moderator note:
Don't double post like that please, you asked yesterday and did not really need to ask any help today... One day is not really enough to call a topic missed by people, and while I understand that you really want help to get this resolved, it really isnt appropriate to double post on this forum, especially when such a small time has passed since you've last posted.