The startup problem sounds very much like you'd expect with bad caps (google it). It's possible it's also causing the other problem, though it seems less likely. First thing I'd do is google bad caps, then use that to check your system.
Sometimes when I shutdown, Windows 7 will stall and just stay on the Shutting Down screen. Sometimes when I boot it, it will stall on the COMPAQ screen for a looong time before it boots. I've done countless hard resets and I'm worried that this will do damage to my computer. By the way, my computer is about 2-3 years old, but my hard drive and OS is brand new.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic