I'm not personally familiar with free or open source data recovery products.
GetDataBack is pretty easy to use and relatively cheap, as far as I know. It's been my go-to tool for about 8 years now in cases of data loss. It's relatively fast too.
Just run it against your drive and I'd imaging that as long as the drive motor isn't failing or the platters aren't physically damaged, you're likely to be able to recover most of your data without issue.
Important: Do not format or begin writing new files to the drive. Any changes to the drive you make prior to running a recovery have a great chance of overwriting previous data on the drive and lowering your chances of a complete and successful recovery.
UPDATE response to comment:
It appears as though your drive is undergoing progressive drive failure. This is serious. If you do not run a recovery procedure on your drive now, your chances of data recovery will continue to diminish.
In order to maximize your chances of successful data recovery, you should place your drive inside two or three new and clean ziplock bags and place it in the freezer for an hour or two. This will cool the drive down and minimize the chances of further damage.
While the drive is cooling, assemble whichever tools you choose to use for the data recovery on your computer.
Remove the drive from the freezer and connect to the computer and run the recovery steps as quickly and efficiently as possible. It is critical that you keep the drive as cool as possible during this process. Leave the computer open and point a fan into the system. Do not place the drive into a drive tray as this minimizes the airflow around it and allows for quicker heating of the drive.
All these processes are to maximize the time you'll have to run the necessary recovery tools and thus maximize your chances of successful recovery.
Best Answer
Rest easy! Although I can't guarantee your hard drives will work, I see little reason why they will not.
There are many factors that wear a hard drive (writing to it, reading from it, turning it on and off, exposing it to shock, et al); but letting a drive sit does not cause wear. And it sounds like how you stored it was very wise.
What does take place is very slow magnetic degradation of the magnetic fields on the platters (estimated at 1% reduction per year). After just seven years, your data is probably fine. The magnetic fields will still have 93% (estimated) of their strength, which is so high that I doubt any bits will flip beyond the capabilities of the built-in error control mechanism.
It's also great that the data is stored on a USB drive. That makes it very easy to use on any computer, and making backups becomes even easier.
Don't be surprised if your computer work as well! It will probably turn on just fine. At that time, you can enjoy spending 10 hours installing software updates for the last 7 years!