If you've (possibly inadvertently) clicked on the 'speaker mute' button in a Youtube video, your browser remembers the setting and plays all other Youtube videos silently until you un-mute the speakers. So go to a random Youtube video and see if it plays with sound. If not, you'll find the mute button underneath the video, just to the left of the slider which lets you advance or rewind the video. (People often accidentally click on 'Mute' when using that slider).
Also check that you've not got the tab muted within Chrome. (As far as I know, it's similar to Firefox, where - when a video is playing - there's a mute button available on the right of the tab at the top of your page. It's easy to click on it by mistake when trying to open a new tab).