My Lenovo Ideapad got soaked, but the hard drive was protected and is still usable. I want to know if I can swap it into any other computer I buy. If not, are there certain computers that I can do this with? Are any computers similar enough to the z585 that this could work?
According to the specifications of your laptop, the drive is a SATA 300 drive, which means you'll have no problem connecting the drive to another computer that has SATA data and power capabilities. This is assuming the drive is not damaged.
If you're not sure about the other computer supporting SATA, here's a comparison of SATA (the drive you have) with PATA (an older form of connection for hard drives):
If the other computer you have has Serial ATA (SATA), you shouldn't have any problems.
One thing to consider is that you do not want to boot from the drive using another computer. The drivers that are loaded into Windows are specific to your laptop. It would be better to boot into another working Windows installation, and copy the files you need from the drive, format it, then use it as you wish.