As we know there are many PC users who bought Metro Redux 2033 are busy in solving Metro Redux 2033 startup issues instead of enjoying gameplay. If you are also stuck into Metro Redux 2033 startup crash mess even after having all the compatible hardware, then these workarounds might help you as well to get Metro Redux 2033 started on your PC successfully.
Verify Metro Redux PC System Requirements first.
Fix 1: Run as Admin
Right click the Metro Refux .exe game launching file and select 'Run as Administrator'. Remember to launch game by it's .exe itself, not via Steam.
Fix 2: Don't Use recording softwares,
Exit all the screen recording software which uses overlay technique to record gameplays, such as Fraps or camtasia etc.
Fix 3: Alter or Delete user.cfg
Altering user.cfg, might work for you, go to "\steamapps\common\Metro Redux 2033", open or edit user.cfg and look for r_res_hor, r_res_vert and r_fullscreen, change resolution to lower such as 800x600 or simply turn off full screen. If altering user.cfg doesn't work then, delete user.cfg, taking a backup first is safe bet.
These solutions are compiled from steam community support for Metro Redux 2033, hope these solutions work for you as well.
Update: Metro Redux PC Patch is released, please update via steam.