The problem is the AMD OpenGL driver crashes the game right after loading a single-player campaign level, or even with newer drivers it can crash when looking at access terminals in the game.
There is an easy fix that will do nothing to the rest of your system except patch Doom 3 BFG Edition. It is as simple as copying an older AMD OpenGL driver into the game's directory so only Doom3 will use this older driver.
You can do this in one of two ways:
A) Download the older OpenGL driver file I've expanded for you:
For 64 bit: Windows Vista, Windows 7, Windows 8http://s000.tinyupload.com/?file_id=01622665446405141409
For 32 bit: Windows Vista, Windows 7, Windows 8http://s000.tinyupload.com/?file_id=00028799409514376260
* Download the appropriate file from above, then drop the "atioglxx.dll" file into the game directory where Doom3BFG.exe is located.
* Launch and run the game normally (no need for anything else)
B) Do it yourself from the AMD drivers
* Obtain the older 13.1 Catalyst drivers for your system. Go to the AMD Graphics Driver site for your videocard and operating system, then click the "Previous Drivers and Software" link on the bottom RIGHT side of the main driver page... then look for the 13.1 drivers. Download this driver set.
* Run the 13.1 installer and CANCEL on the first window after it uncompresses the drivers.
* Go to the C:\AMD\Support\13-1_vista_win7_xxxx_xxxx_dd_ccc_whql appropriate to your system
* Inside that directory, traverse into Packages\Drivers\Display\W86A_INF\B151068 and look for the file: atioglxx.dl_
* Create a writable directory somewhere (for example, C:\Expand) and copy this file to that new directory.
* Open a command window (On the start menu, type "cmd.exe" in the search box, you should see "cmd.exe" appear at the top search results. Click on this to run it)
* You should now be in a DOS prompt/DOS box command shell. CD to the directory where you copied the atioglxx.dl_ file (type CD \EXPAND and hit enter, for example)
* Type at the command prompt: EXPAND ATIOGLXX.DL_ ATIOGLXX.DLL
* It should say the file has inflated or expanded like 127% or similar factor.
* You may close the command prompt now and navigate to the directory (C:\EXPAND) and see both files now: ATIOGLXX.DL_ and the new ATIOGLXX.DLL
* Copy the newly expanded file (ATIOGLXX.DLL) directly into the Doom3 CFG Edition directory in the same place as the Doom3BFG.exe file.
* Launch and run the game normally (no need for Administrator or compat mode).
REMEMBER you have this file in the game directory! In later Catalyst drivers, try removing this file, launching the game and seeing if it's been fixed. This file may NOT be compatible with later drivers after the latest 13.4's so REMEMBER this kludge should the game stop working after updating your drivers down the road.