I too fix my friend PC's and laptops, and even use facebook to find repairs to make some money, the amount of times people have cursed me because I explained to them about how laptops just don't cut it when gaming regardless of the specs, if those specs were in a desktop with a real GFX card you would be fine etc.. One guy (annoying brother in law) got a toshiba laptop even after I warned him, the thing broke 5 times with a dodgy hard drive, he sent it back every time and still wouldn't bloody listen when I said get a desktop. I even offered him an old case and monitor so he would of saved money, but some people just don't accept facts from people who know them.
You could try to put an SSD in; I believe the normal SSD form factor is the laptop dimensions, as size isn't much of an issue at the moment for SSDs. I have one. The performance gains from a good SSD are mind boggling. I recommend the OCZ Vertex 4.
my seven year old computer with a minimalist graphics card and 4 gigs of ram runs PA like a dream but my high grade computer i got a year ago cant even get it running. the alpha stage is so variable that there is no way to say for sure if something will work or not.
Where is your DxDiag.txt? Currently all crashes on start I seen was because of Windows and drivers problems, not because of game.
this is a problem that was dealt with long ago. its just a compatibility issue should be solved later on.