This is most likely a TimThumb related problem. TimThumb is a popular 3rd party script used for automatically resizing images and will work out of the box on most servers, but on others it requires some 'special attention'. By default, the slider uses TimThumb only for creating the thumbnail images, but it's not dependent on this script, so you can disable it from within the Slider PRO -> Plugin Options page. If TimThumb is disabled and you need thumbnail images, you will need to manually create them.
There can be various reasons why a server won't allow TimThumb to run properly. We'll take a look at some of them.
1. Folder permission
Please make sure that the 'cache' folder (/wp-content/plugins/slider-pro/includes/timthumb/cache) has the permission set to '755' or '777' (on some servers 777 is necessary). I recommend checking with your web host what the best permission setting for making the folder writable would be.
If you're using HostGator as your hosting provider, you will need to contact them and request 'mod_security whitelisting'. Please read this.
3. Temporary URL
Another possible problem would be the use of a temporary URL (i.e. http://22.214.171.124/~username/). TimThumb doesn't support temporary URLs, so you might have to disable it until you move the site to a domain name. You can disable TimThumb from within the Slider PRO -> Plugin Options page.
4. External images
If you're loading the images from a different domain than the one the slider resides in, you will need to open the 'timthumb-config.php' file (/wp-content/plugins/slider-pro/includes/timthumb/timthumb-config.php), set the 'ALLOW_EXTERNAL' variable to true and then, in the $ALLOWED_SITES, specify the external domain where the images are located. If you want to load external images from any domain, you can set the 'ALLOW_ALL_EXTERNAL_SITES' variable to true.
If the above solutions don't work, please email me some WordPress and FTP credentials and I'll take a closer look.