Do you want to try to keep the same domain name? If so, if you go in the panel and try transferring the domain to DreamHost, what happens? It appears to be registered in your name, so you should be able to transfer.
If you want to start fresh with a new domain, then choosing one and doing the zen cart one-click should be easy. After that it's learning to add products, etc.
You'll probably want an IP and SSL certificate before too long, or at least some way to take payments?
Have you downloaded and backed up as much as you can of anything you want to re-use from the old site: images, text, etc.
They hired more support help.
Tip me (and DreamHost gets 5%+$0.30) Cut the code: [color=#00CC00][b]9999[/b][/color]=$99.99 Off