The up-side is, I doubt you've lost anything from the database at this point, but frankly, if you've been operating for three years and don't take regular database and file backups, and it's only now become a consideration, well... let's hope that's not true.
Something to check on before going further: It may be as simple as consulting the documentation in your hosts FAQ or support group for instructions on how to enable or switch to php5 support for your site. Then you can probably just run the upgrade routine, or at least do a manual upgrade.
One caveat; depending on how old your version of WordPress was, you may have to do some incremental upgrading to get it back to normal.
Assuming all of your content is still intact, my advice is to take a database backup and secure a couple of copies of it locally before you continue on, just as an insurance policy - on the assumption that there isn't yet any issue with the existing database.
[edit] it might be wise to use your ftp client to download a copy of at least, the /wp-content directory (if not the entire site) and store that as well.