I had the exact same issue. Clips would play in the trimmer window, I could scrub the timeline, but the timeline simply would not play no matter where the cursor head was. Long story short – there is a clip reference in your sequence that is somehow corrupt and causing this. Select half the entire sequence and delete it. Try to play. If it woks then the errant clip is in the bit you just deleted. Undo and repeat this process till you hone in on the single clip that, when present, for some reason prevents the timeline from playing. Delete it from the sequence and you’re fixed.
I didn’t try to re-insert the dud clip onto the timeline in my case (didn’t need to – it was disabled anyway), but give that a try and see if it still works.
In my case it appears to have happened when I dynamically-link imported the clip into After Effects for some comping. The AE sequence was fine, but the original clip which I had kept on the timeline as a backup reference got screwed.