replacing a toshiba hard drive in a mac mini
Yeah it sounds like maybe you just need to install the OS onto it (I guess "it wouldn't work" isn't really defined, so this is a guess).

If Tetsujin's suggestion doesn't work, and you have the older Mac Mini (I know my Mac Mini had the drive die - and it's from 2005, so internet recovery wasn't available), then put a Mac OS CD in the drive and boot up while holding down
    Command + C
to boot from the CD drive.  Then install the operating system from that.

You might also want to make sure the shop gave you back your old hard drive, since it has all your stuff on it.  Depending on how dead the drive is, you could put it into an External Enclosure and try to get some of the data off it. (Make sure you choose the correct drive connection: IDE (older computers), SATA (newer computers I think?), or other types (mSATA etc.).