backup all products?

I really screwed up my Joomla site and might need to start over from scratch. Luckily, I still have access to the backend of my old, busted site.

I'm wondering if there is a way to backup all my products from the old install so I can easily migrate all that work into my new, fresh Joomla install.

The easiest is to export the jos_hikashop_* tables from your database via phpmyadmin and then importing it also via phpmyadmin on your new website.
Then, you can also download all the files in the folder media/com_hikashop and put them on your new website at the same location.
Finally, you can reinstall hikashop on your new website.

Ok, sounds like a plan. Question though, my previous install was an older version of Hika Shop. Would it still work if I installed the newest version and followed your instructions?

It should yes but it would be best to use the same version.