Running the game in Windows 8, 7, Vista or XP you need to set "Run as Administrator" on both softwares, the game and the Origin Launcher manager. To do that go to C:\Program Files (x86)\Origin (for the launcher manager) and look the file named Origin. Right click on it > Properties > hit Compatibility tab > look for Privilege Level at the bottom > check the box "Run this program as an administrator"
Now do the same steps for the game. Go to C:\Program Files (x86)\Origin Games\Mass Effect\Binaries and follow the same steps as before.
If this dont help, you need to replace your graphic card. Simple like that.