Well, I am sorry to say that you will not be able to play the game.
Lara Croft and the Guardian of the Light requires a graphics card the has Shader Model 3. Your Laptop has an older video card, ATI Xpress X1200, which does not support SM 3. Your current laptop only supports up to SM 2.
This is a hardware limitation, therefore the only thing you can do is to buy a newer laptop if you wish to play the game. SM 3 has been around since 2004/2005 so I'm assuming ATI left out the hardware from the X1200 video card to keep costs down since it is targeted at the value segment of laptops.
If you wish to keep your current laptop, then the only advice I can give you is to search for the system requirements of any other games you wish to play for the term "Shader Model 3". If SM 3 is required, then don't purchase it.
Thank you so much for the information. I wouldn't have downloaded it if I had known. The programmers allegedly checked for compatability before download. I'll know next time! Again, thanks for your info. Happy Holidays!