Tom hit the high points about interface. Your final note "not usb" clears up one thing I was going to point out, that any widget that plugs a hard drive into the USB port of a computer is performing translation between two very different interface types.

SATA would be very good (recursively Serial ATA) because it's finally a universal hard drive interface. Look for a small plastic connector, like a big USB connector but with sleeker lines. The key identifying feature is that the row of pins, about half an inch long, takes a short jog at the end, like an elongated "L". In your laptop, it probably would have been connected through an oval-cross-sectioned cable like a double-scale modular telephone cord.

If your drive matches that, then it's worth opening up the PC to see if it uses SATA, and that it has more than one port. Because if there's only one port, it must remain plugged in to your PC's single hard drive for the computer to boot. But if there are two or more ports, even if you have to unplug one of the drives other than the boot drive, you can copy data off the laptop drive.

If you're constrained to one SATA port on your PC, that's when you might want to consider an external enclosure that adapts your laptop drive to USB. BTW, when using USB for bulk data transfer, you really want USB 3.0. USB 2 crawls along when used for external hard drives, but it's better than nothing if that's all you've got.

You would also have to use an external box if your PC doesn't have the same hard drive interface as the drive. Then it's just a matter of searching for a box with the same HD interface on one side, to USB (3) on the other.

It's possible to escalate to higher levels of geekiness, but I hope not.