I have my phone linked to 3 separate gmail accounts. I started getting the "No Connecttion" error on the primary gmail account last night (this is the gmail account I logged into @ the Verizon store when I first received my droid). I tried to delete the account, but the phone wont let you delete the primary gmail account.
Note: Before you try the solution below, I would back up your contacts just to be safe. I didn't lose any of mine, but this never hurts. (Contacts > Press Menu button > Choose Import/Export).
I searched a bit and came across this:
Troubleshooting sync - Mobile Help
App: Troubleshooting sync
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On Android devices, the Gmail application is automatically synced with the Gmail server, and vice versa. If you experience problems with syncing, try clearing your device's Gmail application data and doing a fresh sync with the server.
Just follow these steps:
1. Press your device's
< Home > button, then press
< Menu >.
2. Select
Settings and then
Applications.
3. Select
Manage applications.
3a. (On the Driod, you then have to press Menu again, press Filter, and choose the Show All option)
4. Select
Gmail Storage and then select
Clear data. Answer
OK when prompted.
5. Return to the list of applications by pressing the
< Back > key.
6. Select
Gmail and then select
Clear data. Answer
OK when prompted.
7. Restart your device (Press and hold the
< End call > button, then select
Power off. Press
< End call > to power on).
Your device will re-sync with the server after restarting (this may take several minutes)