Strange that your UnrealTournament.log is empty.
To start change that line
into
this will speed up the UT startup
Then change that line
WindowedViewportX=512
WindowedViewportY=384
WindowedColorBits=16
by
WindowedViewportX=640
WindowedViewportY=480
WindowedColorBits=16
in the case UT want to load in windowed mode and that 512/384 is unsupported by your monitor/radeon
Then change this
FullscreenViewportX=640
FullscreenViewportY=480
FullscreenColorBits=16
into this
FullscreenViewportX=800
FullscreenViewportY=600
FullscreenColorBits=16
in the case your Radeon do not like 640*480 in fullscreen when using OpenGL
Then find this
[OpenGLDrv.OpenGLRenderDevice]
Translucency=True
VolumetricLighting=False
ShinySurfaces=True
Coronas=True
HighDetailActors=True
DetailTextures=True
Replace those few lines by the following
[OpenGLDrv.OpenGLRenderDevice]
Translucency=True
VolumetricLighting=False
ShinySurfaces=True
Coronas=False
HighDetailActors=True
DetailTextures=True
TruFormMinVertices=0
TruFormTessellation=3
UseTruForm=False
AAFilterHint=0
NumAASamples=0
UseAA=False
RequestHighResolutionZ=True
MaskedTextureHack=True
FrameRateLimit=0
SwapInterval=1
UseVertexProgram=False
UseCVA=False
UseMultiDrawArrays=False
TexDXT1ToDXT3=True
DynamicTexIdRecycleLevel=100
UseTexPool=True
UseTexIdPool=True
UseSSE=2
BufferClippedActorTris=False
SinglePassDetail=False
ColorizeDetailTextures=False
DetailClipping=False
UseDetailAlpha=False
RefreshRate=0
MaxTMUnits=0
NoFiltering=False
MaxAnisotropy=1
UseTNT=False
Use4444Textures=False
UseS3TC=False
UseAlphaPalette=False
AutoGenerateMipmaps=False
UseTrilinear=False
UsePrecache=False
AlwaysMipmap=False
ShareLists=False
UsePalette=True
UseMultiTexture=True
UseBGRATextures=True
UseZTrick=False
MaxLogTextureSize=8
MinLogTextureSize=0
MaxLogVOverU=8
MaxLogUOverV=8
OneXBlending=False
GammaCorrectScreenshots=False
GammaOffsetBlue=0.000000
GammaOffsetGreen=0.000000
GammaOffsetRed=0.000000
GammaOffset=0.000000
LODBias=0.000000
DescFlags=0
Description=
CacheStaticMaps=False
Use16BitTextures=True
Notice the line
Change it to your refresh rate, as some people reported problems with 0 (normally it is supposed to detect your refresh rate automatically)
So if your monitor refresh rate is 85hz , just replace it by
RefreshRate=85
This should get you started (but be sure to be in version 436 or the enhanced OpenGL should have lot of difficulties to work)
In the case it always does not work, restart Safe mode and change to Direct3D (with all the previous modifications)
A question to finish , have you ever succeeded to play UT in Direct3D or OpenGL before ?
If yes, it could be a ATI driver that you have installed recently that is not UT friendly.
I assume of course your system has no virus/spyware etc... as i assume you have checked your system first before asking for help here.