With full control correct? Do any of those groups have deny?
I know lot of questions, but these things make a different. Permissions are additive, so you get the highest level permissions granted when you compare NTFS and share folder & file permissions. The exception is deny, deny overrides anything. So if you are part of a group that you explicitely said deny to you won't have access.
You didn't mention the server version, if you go to the share locally and go to permissions, there is an effective permissions tab. Check your account to verify windows 'believes' you should have full access.