I found this fix to after pressing play crash.

So with me, whenever I would press play it would go black. Then a black screen would appear for .5-1 seconds then go away and Sw:tor would not be shown as running the fix that I found was 

1) windows button + r 

2) C:\Users\%USERNAME%\AppData\Local\SWTOR\swtor\settings

3) Press Ok

4) Go in client_settings

5) Paste this

[Renderer]
Buckets = 2
D3DFullScreen = false
GraphicsDeviceId = 26815
Height = 1024
MeshLODQuality = 1
NativeHeight = 1420
NativeWidth = 1980
PerformanceLevelChanged = true
TextureAnisotropy = 16
Width = 1280

6) Press alt+enter for window mode to put screen to you desired width height.

Hope this helps!