Does this happen with a brand new project? In other words, try this:
1. Click file - new
2. In your brand new, clean, veg file, drag a media file onto the timeline
If the audio plays OK, there is something muted on your project file in question (or something about the file is suspect)
If audio is grayed out in this new project, then we need to keep looking.
I would suggest following David's suggestions first. If, as he said, the audio in the new project is still grayed out, go to Options > Mute All Audio. Make sure this button is disengaged.