Transitioning from WordPress 3.2.1 to 3.5.1

Good afternoon,

I am having some troubles recovering a website at a new company I have started at. A rather old website is still on WordPress 3.2.1 software, using the minimal theme, therefore meaning I am currently unable to make any changes to the website other then text content.

How do I move the website on the new WordPress 3.5.1 software?

I have tried the suggested FTP routes with Filezilla and had no success, the website did not appear and I had to load the back-up. Is their a simple way to do this with cpanel for example? My host is hostgator if that is relevant.

Thanks for the help!