Please run the game from the command line (cmd)
Example: java -jar d:\Games\Tachyon\Client\Tachyon.jar
It should show the error message.
Post the error message here, then I can try to help.
(This is what shows up...)
[Client] Loading client parameters
[Client] Client config file C:\Users\Owner\config.cfg not found!
Exception in thread "LWJGL Application" com.badlogic.gdx.utils.GdxRuntimeException: OpenGL is not supported by the video driver.
at com.badlogic.gdx.backends.lwjgl.LwjglGraphics.createDisplayPixelFormat(Unknown Source)
at com.badlogic.gdx.backends.lwjgl.LwjglGraphics.setupDisplay(Unknown Source)
at com.badlogic.gdx.backends.lwjgl.LwjglApplication.mainLoop(Unknown Source)
at com.badlogic.gdx.backends.lwjgl.LwjglApplication$1.run(Unknown Source)
Caused by: org.lwjgl.LWJGLException: Pixel format not accelerated
at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)
at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(Unknown Source)
at org.lwjgl.opengl.WindowsDisplay.createWindow(Unknown Source)
at org.lwjgl.opengl.Display.createWindow(Unknown Source)
at org.lwjgl.opengl.Display.create(Unknown Source)
at org.lwjgl.opengl.Display.create(Unknown Source)
... 4 more
Exception in thread "LWJGL Application" com.badlogic.gdx.utils.GdxRuntimeException: OpenGL is not supported by the video driver.
Well that's pretty clear - your video driver does not support OpenGL.
I have the same problem on my old NetBook.
Sadly I don't know how to solve this. Because it is not code related, but rather related to the video driver.
I can only suggest that you search on the net for solutions for this problem.
If you find one, please post it here.