Will desktop and hard drives stored for 7 years still work?

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!