Website project canceled. Do I need to Restore old page?
You seemingly do. This is equivalent to taking your drivable car to the mechanic for maintenance or improvements. If the contract is cancelled for whatever reason, it would be unacceptable that the mechanic returns you the car in a condition worse enough that you can no longer drive it.
The transfer of domains & credentials to your server supports the presumption that you are responsible for the contents and functionality of the site for as long as the domains & credentials are under your control. To the act of returning what was given to you is attached the expectation that you would restore it to its former state if the contract is cancelled or rescinded.
An alternative scenario helps making the point. Suppose you cancelled the contract upon realizing you are not proficient enough to create the website. It would be nonetheless reasonable to expect you to bring his site back to its original state. Absent a clause addressing the event of cancellation or rescission otherwise, there is no reason why your responsibility in this regard would depend on the cause for rescission.
Furthermore, the formation of the initial [verbal] contract tends to indicate that you are more proficient in the matter than the client. This places on you the burden of taking sufficient precautions by directly securing a backup or at least requiring your client to create one. The fact that your backup got corrupted is rather tantamount to not having done a backup at all.
Something that might favor your position is the common practice that many IT service providers recommend that users always have a backup, whence at this point average person "should not" (?) need to be reminded to do backups when transferring his data or systems to a provider. This argument might not be strong enough to release you from your responsibility to secure a backup for yourself, though. The stronger the client's expertise in IT matters, the likelier that his failure to produce a backup will release you from having to restore the site (the mere fact that the client asked you to create a website does not conclusively preempt the possibility that he might also be proficient in the matter).