Did you try setting windowed mode to true in your eqclient.ini file? I don't have the exact config line you need here, but I can probably provide it here later if needed. If your issue is with resolutions, you should still be able to run fine with windowed mode on.
BTW, do you know the native resolution of your laptop display? Is it something unusual? Are you able to adjust it to older more standard resolutions like 1024X768 and see if that works? Normally if you can get it working in a standard resolution, you can play with it after and get it working in a normal resolution for you.
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