Ouch.
The partitions are likely linux types that Windows can't read. You would need to plug the drive into a computer running linux, or, failing that, boot the PC into a linux recovery CD/USB such as SystemRescue. However, if you're not proficient in linux, you should probably leave this to others to do.
If you're in contact with IT, can they make a disk image available for you to download? If so, it might be not-quite-so-difficult to copy that disk image back over your existing internal hard drive. Again, you'd need linux rescue tools and proficiency, but at least you wouldn't need to worry about trying to rescue data off potentially unrecoverable disk sectors.
Alternatively, the other alternative would be to have them send you a new hard drive.
Ouch.