if the cd-key is not the problem then some1 banned you for good.

about pure yes .. you are not pure meaning you have stuffs in your quake 3 that makes your client unpure: fancy images , weapons, other fonts .. every1 can see this in your image you posted above. (fancy images + other fonts)

if you are unpure you wont be able to join any server with pure on. but thats something else then to be banned.
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epsislow

yes u installed "HQ mod for q3", for removing this mod you need to delete "pak9.pk3"
this mod is cool for watching demos