new domain old database?

Hi, I was doing a lot of blogging a couple of years ago and through some stuff up lost my domain. I got disheartened and gave up blogging. Just the other day I decided to start again. I took out another domain very similar to my old domain (as my old domain is now available again but now as a premium domain costing too much money). I think I have found on my host (hostgator) an old back up of the old site. My question is…… can I restore this old back up to the mew domain?
I am not a complete numpty when it comes to computers but I’m no where near an expert at this type of stuff. So would it be something that is quite acheivable by someone with fairly basic skills, or should I just start from scratch? I don’t care if links etc don’t work, I would just love to retrieve my old posts I wrote myself. Thanks heaps ??