After OS system recovery, how to get lost files?

I have an Acer that underwent the 'infinite startup repair loop'. So what I did was when Acer eRecovery 'backed up' my data, I used a USB loaded with Ubuntu and recovered that backup (what I should have really done was just get the files I needed, but it's too late for that and I'm hitting myself over the head for not doing that). So now, I have a 'new' system and a bunch of .dat files that I have no idea what to do with, so I'm crawling through cyberspace trying to find someway to possible retrieve those files, anyone?

(Unless someone knows how to work eRecovery and be able to restore my data that way)