1. DO NOT SWITCH ON with the heat sink removed - you get about 10 seconds before the BGA is killed if it has no heat sink attached.
2. Does the computer appear to be functioning apart from the video? Do the keyboard LEDs toggle when the Num Lock and Caps Lock keys are pressed?
3. It is possible the internal video is disabled in the BIOS but obviously you can't see the screen to check. Look for a jumper, usually near the battery (behind the blue socket) marked "CMOS Clear", move it to the other position for a few second then move it back. This should wipe any configuration settings and restore the default ones.
If the BGA has died, and if the rest of the PC seems to be working, I wouldn't recommend you try changing it. The chances are you won't be able to get a new one anyway but even if you did, special equipment is needed to remove and replace it. It isn't something you can do at home. It would be far more sensible to plug a new video card into the slot and use that instead. If that gets it working, change the BIOS settings so the internal video is disabled, this will also probably release quite a lot of memory back for program use.
Brian.