If this 'touchsmart' computer is an all-in-one (computer components are built into the monitor, there is no separate box) then no, you can't upgrade your graphics card. All-in-one computers are basically immobile laptops, very little is upgradeable, largely due to lack of internal space.
If this computer actually does have a tower, odds are you will have to upgrade the power supply. Most prebuilt systems do not have power supplies adequate for running high end graphics cards.