This is most likely an error with how you’ve installed WordPress on your server. Did you install WordPress yourself or did someone help you? As just a general guess I would say most likely your uploads directory is not writeable, or possibly there is some sort of other issue with your host. If they offer any general support for WordPress, you may want to try contacting your web host customer support.
The only way I could think that this issue could have anything to do with the theme is if, theoretically, the theme registered too many image crop sizes, and when uploading an image your server just doesn’t have the resources to create all of them. You could confirm whether this is the case or not by activating the WordPress default Twenty Twelve theme and seeing if you could upload images with that theme.