What will I do with the android games?

My mom have a T-Mobile HTC that has been given to her recently and its from Hawaii. Now I would like to play some android games. At first I know that I should download at the marketplace. But when I try to open it, it says problem with the marketplace service. Then I tried to download from the internet (PC) but when I tried to install it, its says 'No appllication associated with _(file name)_'. Help pls! But when I try it on other phones it works fine. And theres no options about 'Allow non-market apllications' . oh And I know I have few misspell. :D