First thing I would do is make sure you have the most recent drivers for all your hardware, update them if neccessary. If this doesn't solve some/all of the problems, call where you got your computer from and tell them what's wrong, could be defective stuff. Also make sure to get rid of all the crap that comes pre installed on the computer.

I assume your running a version of Windows XP. Warcraft III worked for me when I installed it on XP Pro.

It could be countless factors affecting the performance of certain software on your computer. Best bet is to call the store. Hope you get this solved soon, it sucks having to beat yourself over the head because of a new computer.

EDIT: When you run or try to run the software does it give you any error messages? Post some of them here if it does.