The only .mov files I have are the video clips from my Kodak Digital camera.
Today I uninstalled Shark's Codec pack v2.7.3 and before installing v2.7.4, I checked and found that I can play these .mov files both in WMP and WMC.(without Shark's codec pack). Of course I am running 32bit Windows 7 but it shouldn't be different with 64 bit.
I scrupulously avoid any other codec pack (other than Shark 007's) and/or media players -the only exception being DivX of which I have a licenced version.
IMO, it will be difficult for anyone at a distance to categorically pinpoint why your system does not play this or that format. On computers we may not remember the many things that we have done to it or on it, just after a few weeks, especially when one keeps on experimenting. Many a times I had tried to keep a log but failed miserably.