Hmm: I don't have quite enough information here to go on, "Jenny".
When you say "Partially boots", what do you mean? Does it complete if you leave it? Do you get an error?
How, specifically, did you create and restore the backup?
If you boot with the Option key held down, can you see the OS X OS as a choice, select and boot from it?
Any additional information you can supply will help diagnose the problem you're encountering.
(Note that it might be better -- but isn't required -- to do this via email by sending the information to support-at-shirt-pocket.com. That way, I can log it in my own support database, and we won't bore people with the intermediate details. Once we reach a conclusion, we can post it here.)
Thanks!