I'm in the same boat too. I just realized it now. Can't spectate any game at all. I tried a repair but that didn't fix it. I might try to uninstall and reinstall. I'll post back if that fixes it.
Never used LoL replay.
Windows 7 (64bit)
250GB Samsung Evo 840 SSD.
2GB Nvidia Geforce GTX 670 - Driver Version 347.25 - Geforce Experience 2.2.2.0
League of Legends 5.1.15_01_09_17_50
Verizon FIOS, Maryland
UPDATE:
Uninstalled and reinstalled the game. Thought there was progress, since instead of a black screen and a blue circle mouse cursor, there was the Champion loading screen. Then, I tried to click while the Cursor was still a blue circle and I got to the spectator mode but no one was moving and the minions were all standing still. I noticed I can rewind and there was approximately 2 minutes of game I could watch but it didn't go beyond that. Then after a while a window popped up and said. "Connection to spectator server failed. The game will now exit."
UPDATE 2:
I tried spectating another game and I got inside the spectator mode but there aren't any players or creatures. Just a timer counting up. Then, a dialogue box came up and said, "Unable to download spectator data. The game will now exit."
UPDATE 3:
The 5.2 Update seems to have fixed the spectate problems for me.