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Install Star Trek Online via Steam.
Make a new shortcut to open Star Trek Online.exe instead of starting the game through Steam. (Saves system resources.)
Run and update the game via the launcher.
Start game. Wait +/- 15 minutes while it tries to find the optimal settings for your system.
Exit game once you're in the character choice menu.
Start game anew. Launcher should not have to patch again.
Once the game hits the Star Trek Online - Delta Rising logo screen, it will still take +/-5 minutes before it suddenly gives a D3DX9 render error.

I could not find this particular error in the log, but the log is rife with other issues that may need looking at.

Here is the log:

https://www.dropbox.com/s/6jwxl9y9ave3h6e/2015-04-08%20Star%20Trek%20Online.log?dl=0

Edited by Maki

What is odd is that I have had tha that happen randomly, specifically when I was moving the window around or switching focus between that window and another. I am not sure what causes it, but it actually does work just fine. What type of graphics card do you have? What drivers? I am running an Nvidia card with the proprietary drivers. If you are running something different, perhaps there is a goof-up in the driver or some sort of conflict. You might want to look at opening a ticket with WineHQ. The screenshots came from my system, so I know it works there, but Wine can be picky, especially with certain graphics cards or drivers. 

Please use pastebin to post your log. I don't want to download anything. lol. Wine spits out a lot of what look like errors, but usually can be ignored (like almost everything that says fixme.).