If there are no back-end scripts, you should be able to grab the entire web site.
1) get established with a new hosting provider -- ask provider to give you a temporary host name from their domain so that you can verify your web site data after upload
2) get backed up web site, upload to new provider and test
3) change DNS servers
4) advise original hosting site that they are no longer authoritative for your domain
5) tell developer to take a hike