You don't have to worry about your harddrive hurting your new Xbox. The problem that created the so-called red ring of death was not any kind of harddrive issue - rather, it was strictly that Microsoft put a tiny fan in the system. The Xbox 360 has a massive cpu (3.2ghz multi-core Xeon), and that generates massive heat. So, the fan wasn't strong enough, and the internal mechanisms were actually melting!
Don't worry, your harddrive is fine.