You can replace with any Xbox1 dvd drive, there's no firmware/keys to worry about with the originals..they have hard drive keys instead of DVD keys. My recommendation is to find a Toshiba, if I remember correctly those seemed to be the quietest and most reliable of the originals, but it's been a long long time since I touched original Xbox stuff. I'd offer to give you my spare drive for the cost of postage but I'm letting my neighbor use it for a presentation at his kids' school, and don't know if the tray works or not anymore.
Might be cheaper to check an online auction site like eBay for someone selling a broken/no power Xbox, the drive is likely still good and sometimes it's cheaper than buying the drive by itself for whatever reason.