Probably, but it's Microsoft, so there's always a chance something will go screwy.
You'll also have to reload any games you may have saved to the hard drive, or any content you downloaded won't work. Saved games and your XBL account info should probably still be in tact.
Also, not sure if it's all that cost effective, but you might want to call the Xbox support line and ask them about their no-questions asked repair options. Pretty much everyone has them. You send in your unit, pay some fee, and then no matter what's wrong with the system, they'll fix it. You can also see if they can look up your info based on the serial number of the system. It's at least worth a shot before you go spend money on a new system.
I have the Xbox 360, the 20GB verson, and I got the E74 error, Thats the hard drive error it hase one red ring, and I took my hard drive and replaced it with my friends and it said the same E74 error.
I created this problem when I was in a middle of a Xbox Live match and I took the hard drive out in the middle of the game, I know that was really stupid, I just wasnt thinking.
I lost my information to my email that I registered my Xbox under, and I made it under a Yahoo email instead of a Hotmail Email. So I cant send my xbox in with out my account information, so I am forced to get a new Xbox.
I'm pretty tight on money right now so, I was wondering if I would be able to get a Xbox Acrade and put my old hard drive in the Arcade, and still able to register the Xbox Acrcade with a new Email, and make a new Gamertag and account.
Would I be able to do that?