I Have the REAL Fix (without deleting, reinstalling, etc)
I have had the same problem myself for a couple hours of MADNESS, and fixed it.
Step 1: Load Up STEAM
Step 2: Right Click Garrys Mod And Click “Properties”
Step 3: When A Menu pops Up, Click “Set Launch Options”
FINAL STEP: Now, type “-dxlevel 81” (No Quotes). GMOD Works!
This also works with people who have the error pop up on their screen stating “hl2.exe has encountered an error”, or something related instead of it doing nothing, which was orignally what I had to look up to find this solution. Looks like YouTube saved me again.