The answer to 'garbage disposal won't flush' is that the disposal is likely clogged or jammed, preventing water from draining properly. This can happen if the disposal is overloaded with food waste, or if a foreign object gets stuck inside. Common symptoms include the sink not draining, a gurgling sound, or water backing up into the sink.
To troubleshoot, first try using a disposal wrench or Allen key to manually turn the blades and dislodge any blockage. You can also try using a plunger to clear the clog. If that doesn't work, you may need to disassemble the disposal and remove any debris. However, if the disposal is severely jammed or you're not comfortable doing the repairs yourself, it's best to call a professional plumber to diagnose and fix the issue.