Don't Starve won't launch

Hello @jiuhboy, welcome to the forums. Simply based on your log files, it seems this is more likely an issue with your graphics card. Notice error shown:

[00:00:01]: ERROR: Missing Shader 'shaders/font.ksh'.

Which leads me to believe you should instead try to get the latest NVIDIA driver for your graphics card. Although I can't guarantee of it working, but might as well try.

Hello. Have the latest driver version. Reinstalling don't help. Same error: Missing Shader 'shaders/font.ksh'.

 

That error is indicating that one of the installed files is missing.

In steam, right click DST and select properties. In the Local Files tab, click "Browse Local Files"
Make sure this file exists: \data\databundles\shaders.zip
- If that is not there then steam is failing to download the files for some reason
- If the file is there then open shaders.zip and make sure \shaders\font.ksh is there. 
- If font.ksh is missing then delete shaders.zip and then validate your game files again via steam