It could be the case that it's trying to start with an unsupported resolution.
Open up eqclient.ini in your Everquest directory and add the following commonly supported options:
under [Defaults]
under [VideoMode]
Code:
Width=1024
Height=768
WindowedWidth=1024
WindowedHeight=768
FullscreenBitsPerPixel=32
FullscreenRefreshRate=60