I'm not qualified to fully assess FRST logs, but I do see you have Carbonite. You should be able to restore your data using it. I also see you have some restore points available, so Shadow Copies may be available.
I did see some controller errors about your hard drive - this is miscellaneous to the problem at hand, but I would definitely get your hard drive tested to make sure it isn't failing.
What ransomware were you hit by? We need to know what extension was added to your files, and the ransom note. You may use the service in my signature to identify by uploading an encrypted file and ransom note. You may then report back here with the result. If ID Ransomware cannot identify, you may post the case SHA1 it provides for me to manually inspect the files submitted.
If you are looking for assistance with malware removal, you will need to follow the instructions in the Malware Removal or Am I Infected forums. This forum is for assisting with information on the ransomware, which we cannot be determined directly from a FRST log.
I don't see much sign of an infection or ransomware attack from that FRST log, but take that with a grain of salt, as I am not part of the Malware Response Team, so I have not been fully trained on interpreting FRST logs.
Edited by Demonslay335, 02 July 2016 - 11:41 AM.