I got a new Droid on a new Verizon account on Monday 11/23. I set up Sync with my company Exchange account before I even left the store, and had no issues with sending or receiving mail, or the corporate calendar.
Over the succeeding days, the "p" and "k" keys on the hard keyboard stopped working. I called the local Verizon store last night and they offered to replace it. I downloaded and installed MyBackup Pro and backed up my apps and data to the SD card. At the store, I put the new SD card into the phone, as soon as I logged into my GMail account, MyBackup restored all my apps and settings. What it apparently won't do is restore my e-mail accounts. I re-added my Exchange account and one personal POP3 account. The POP3 mail downloaded, but I got nothing from the Exchange account. I deleted and re-added the Exchange account several times, with the same results.
I can send mail on the Droid from the Exchange account with no problem, and it shows up in my sent items when I check it from Outlook or OWA. I receive an initial sync of my corporate calendar, and calendar items I add on the Droid show up in Outlook and OWA. Calendar items I add in Outlook or OWA don't show up on the Droid. If I add a calendar item on the Droid, it then appears to force a calendar sync and I get the missing items. The same is not true for e-mail: sending an Exchange e-mail doesn't refresh my inbox. I've sent a dozen messages and the inbox is still empty.
The Motorola Corporate Directory app works fine.
I'm also the Exchange administrator, so I know my settings are correct (if I change any of them, like an invalid password or server name, I do get an error). I did configure the account as Exchange, as we don't offer POP3 or IMAP. I have the account configured for push e-mail, but I never get anything in my inbox. I left the account configured overnight, and I did get incoming Exchange messages but they didn't sync to my phone. If I select Menu when in the Exchange account, the only options I have as "refresh," "compose," and "accounts," and none of the Exchange-specific options I had before.
I'm really at a loss on this. Does this sound familiar, and if so, what did you do to resolve it? In the interim, I'm going to try adding another Exchange account to see if it's account-specific or a more general Exchange problem.