Looking at it 'from a distance' it seems your new WP 'cannot find' the pictures.
A. Create a back-up of the old website
- using FTP make a back-up files of of the old website on your PC
- make a back-up of the old database!!! Dashboard > Tools > Export
- Choose 'all content' and click 'download exportfile'
An exportfile will be saved onto your PC.
B. Filling the newdomain database with the data from the exportfile.
- open newdomain.com/wp-admin
- dashboard > import > wordpress
- [if required] Install NOW to install the import-utilty
- click 'activate the plugin and run importer'
- choose the exportfile and run the import
You should now have the original CONTENT, not the looks.
C. So a few questions / checks to identify the possible causes / solutions.
- == == == very important == == ==
Use FTP to BACK-UP the file wp-config.php of the NEW site to your PC == == ==
Careful now! Proceed only after completing previous step succesfully!
- Using FTP: Copy the entire OLD site to the NEW destination. Overwrite all files. DO NOT open yet...!
- copy the back-up of the
wp-config.php of the NEW site, overwriting the old file.
Unless I have forgotten something in this list... You should have a complete transfer...
Your site is now ready to be used and tweaked further.
Make sure you make back-ups.
Don't make any changes to a theme itself. Instead make the changes to a childtheme. Should the author of your original theme update the theme, your changes will not be overwritten. Your site with your adaptations will remain intact.
(see: http://codex.wordpress.org/Child_Themes )
Suggestion: use the 'one click childtheme plugin'.