I don't hang out here, so I won't be able to get into a discussion about fixing this (see if the Seagate site has recovery software), but if and when you do get it fixed, get another external HD (bigger ones, up to 3 TB, USB 3.0, are down to $120 on sale [www.NewEgg.com, Costco] - [www.bensoutlet.com has a bunch < 1 TB cheap right now too]) and keep the 500 GB as a loaner to put stuff on for others to take and copy stuff from, or visa versa (like a large flash drive). Get two larger ones so you can keep everything backed up (AllwaySync free version is good and easy to set up and use).
Try recovery software that locates lost partitions. I can't recommend any, as I haven't lost any partitions, but try www.techsupportalert.com for free software, and google around for reviews and tests of the specific software before you use it, as I've read that it is possible to permanently lose the partitions if the software is bad.
You can try removing the shortcut you see in the root of the F: and G: drives. It is also possible that just mounting the drive on your system has infected it as well. Do run advanced A/V and Anti-malware scanners on your system now. Whether or not you can recover any of your data remains to be see. FWIW, I NEVER lend my hard drives to others. When I lend them a thumb drive, I wipe it completely, and create a new boot sector on it with a Linux system before I remount it back to my Windows environment.
Yes, I'm using Active Undelete FULL version and it was able to show me all the files from M to Z. I'm able to retrieve them but the only problem is any file larger than 71.44mb ends in "error" and I can't save those files.