Xbox 360 crashing at start-up, possibly update-related

Hello, I've been having problems with my 360 and I was wondering if anyone could give me a hand.

I recently put the game Left 4 Dead 2 into the console and it required an update, so I allowed the console to do so. However, when I thought the update was finished (it came up with the logo and boot-up noise etc.) I removed the disc, which I think may have disrupted the update.

I recall coming to the dashboard and finding the 3D avatars of my profiles blacked out. After continuing on and selecting my own profile, then returning the disc and trying to play, the system crashed.

Every time I've booted up the system since then has had many different results. With the Left 4 Dead 2 disc in, the console gets to the logo and the "XBOX 360" text underneath it, then freezes. Without the disc, it only gets to the logo and the text does not appear and it freezes. I have also tried removing the hard drive with both combinations; when the hard drive is out and there is no disc, it comes to a "Failed to Update" error screen (which leads me to believe it's trying to update, but is unable to). When the hard drive is out and the disc IS in the drive, I get the same results as when the hard drive is inserted.

If anyone can give me some advice, please let me know.