It's possible that your Farm account was removed from the required groups after the last time that UPS was provisioned.  Please make sure that the Farm user is in the following groups on the local servers and try starting the service again.

Administrator
IIS_IUSRS
WSS_ADMIN_WPG
WSS_WPG

Also, check out this blog post for some troubleshooting steps.  The first error/solution about giving the NETWORK SERVICE rights to some SP folders is key...

http://egroup.jasonmangone.com/sharepoint-2010-user-profile-sync-errors