I was playing in non-ranked, but I'm still frustrated that this happened.

I started up a game using my Mage deck and found a Priest to play against. When we both had 17 cards left, he had the upper-hand but I had the perfect plan for a comeback which would've actually worked.
Then, when it was his turn, nothing happened, for about 5 minutes straight (I timed it after he wouldn't go). Since the "bomb" timer wasn't showing up, I assumed it was lag, but on his part and not mine, as I ran a speed test that stated that my internet was working at normal speed (the speed test doesn't affect my internet at all, in terms of bandwidth).
After the 5 minute window was over, he suddenly sprung to life, and he was moving cards around extremely fast. I heard a "bomb" sound assuming that his turn was up, when in fact MY turn was up, yet I had no chance to play any cards or decide on what to do. So he went through his turn a second time and I heard a "bomb" sound a second time, indicating that maybe he ran out of time, but MY turn was up again, yet I didn't have the chance to play anything. This happened for a 3rd turn of his and mine was up once again evident by the third "bomb" sound. After 3 back to back to back turns, he had a full set of minions with increased damage on the field with me wide open for an attack. He easily destroyed me.

Why did this affect me and not him?

Here are some screenshots that I took before this occurred in roughly 30 seconds time:
http://imgur.com/S9Iu02V
http://i.imgur.com/9t1US0I.png