I had this problem along w/ not being able to get any notifications to play...I'm guessing it's app related. I resolved it by doing a hard reset. I know it's not an option that most people like, but it worked for me. I restored only the apps I really use and haven't had this issue yet. Every time I install a new app I immediately check to see if my notifications sounds will play. I haven't figured out which app was causing this.
To get the original "Droid" sound at startup you need to do the following:
Settings > Sound and display > Notification ringtone and select Droid.
The "Droid" sound will now play when you start the phone however any notifications will now also play that sound unless you set individual notification tones for each app/email account that creates notifications.