Mail not syncing???

My iMac has been sitting turned off for a week.

I've been using MBA, iPhone and iPad all week.

Now that I'm home, I've fired up the iMac... Mail shows dozens of messages in the inbox that I either moved or deleted on one of the other devices. I restarted the iMac. I took all accounts offline and back online. No love

I did look at iCloud web mail and it is fine.

What do I need to do to force a sync of apple mail?

Thanks

Tom