I'm not sure if I'm posting this in the right forum, but it appears to be an account issue, and not a hardware issue.
I originally posted this thread: http://forums.xbox.com/xbox_forums/xbox_support/f/7/t/81302.aspx in the "Using my console" forum, and got no responses. At least none that directly related to my problem. After some fiddling around while disconnected from Xbox Live, I decided to try logging into my roommate's account, which he has recovered onto my console. I signed out of my profile and into his, connected the Xbox to the router, and logged onto Xbox Live. I was able to navigate menus, start up games, etc. with no problems.
After reading another thread somewhere that I can't remember now, I thought perhaps my account was somehow bugged, and attempted the fix posted there: delete the profile from my harddrive, then recover it. I tried that, and as soon as my profile started downloading, the entire Xbox rebooted itself again. I now had my profile name, without any achievements or profile picture. While somewhat disheartening, I thought that's at least better than nothing, until I realized I wasn't able to connect to Xbox Live.
I re-deleted the profile, and re-recovered it. This time the recovery went smoothly, until the progress bar was at about 95%, then the Xbox rebooted itself.
Then it rebooted itself again once my profile auto-signed in.
And then it rebooted itself again once my profile auto-signed in.
Is there anything I can do to fix this? I recently renewed my Xbox Live Gold subscription, and with Gears of War 3 coming out tomorrow, I was really hoping to hop into 4 player co-op with some friends.
As it is, I can sign into my Xbox Live account in offline mode, but playing games solo and not being able to have an official record of my achievements due to lack of an Xbox Live connection really sucks.