If all you want to do is get the Data off it, you could try this.
Mount it inside the Case and disconnect your CD/DVD Drive and use the IDE Cable and Power Cable from it to hook it up as a Secondary Drive.
It should show up as D: if C: is your Main Drive, even if you have Partitioned your Main Drive, then just copy and Paste what you want onto your Main Drive.
If it doesn't show up go into the BIOS and select Auto on the Secondary Drive and try again.
It doesnt have to be actually mounted, if there is no room for it, but make sure it is upside down and earthed to the body of the Computer.
When I do this, I just lay the Tower on it's side with the cover off and set the extra HDD on it's back in the metal. With others put the Monitor to one side, open the Case and lay the HDD on it's back on metal.
If it is a Laptop? I am not sure.