Hey, resnico93! It sounds like StarCraft hasn’t picked up the 1.22.4.5959 update yet. There’s been discussion on the game is running, on this thread. Opening up Task Manager (CTRL+SHIFT+ESC) and closing Starcraft.exe (32-bit) should bring up the Play button again. Otherwise, a reboot will restart these services.
If there’s issues with picking up the Version 1.22.4.5959, try clearing the cache and tools, then reinstall the Blizzard Application.