The good news is that typically these types of external drives are just casings with a regular hard drive hidden in them, plugged in to a converter. I don't know your model offhand, but with the warranty expired and people's personal data all over it, you're probably just going to have to take the chance and pry it open.
Assuming the drive itself is okay, then once you retrieve it it's a pretty simple matter to get an external drive bay or just plug it directly into your computer and get your files. I can't speak to your specific model but a quick Google leads me to believe your Seagate isn't any different.
I'm not going to be the guy to tell you to do it, just throwing the option out there. Provided the hard drive itself is undamaged though all you need do is retrieve it safely from the casing and you're fine. Depending on the connections a simple USB dock will do the trick as far as getting to your files.
I use this one.
However being a CPA and all, you need a solid long-term solution for local backups, it's not a big investment relative to the importance of your data. There's a fellow accountant in my area that had an actual drive failure, he had to ship it off to a special recovery service at a tremendous cost, they actually opened the hard drive itself to do it. Not the way you want to go. Even going with two hard drives and the device above you'd be in good shape, it would work just like a backup drive only you could swap any drive in and out of it as needed.