To answer the original question in the heading - no you cannot restore to a very specific date. Having said that - if you have multiple backups - you can pick the one that you want to use to restore from.
If I understand you correctly, you have no backups in iTunes since you said that you never synced prior to the "stuff up".
I will assume the reference to "connect to the remote server" is about iCloud. If you backup to iCloud you will have to erase all content and settings on the iPad and restore from the backup on the device. You will have the opportunity to select from multiple iCloud backups as well, if you have multiple backups in your iCloud account.
Before you do anything, have you ever backed up to iCloud? - do you have backups in iTunes? If you haven't backed up to iCloud - then you have nothing at all from which you can restore.