Hello Adrian,
Well there are a few things that could be going on that you are getting a black screen after installing your new memory. I would need a little more information to fully help you out. But there are some things that you could check without that extra information.
It seems like this is the right form factor for the memory stick, but you said you added it to the extra slot. So if you still have your old stick in there also i would recommend to take that old one out and just try the corsair memory stick only. If that fixes it it was your old stick that went back. Also when you're adding the memory make sure that they are firmly set into place.
The thing that I think might be your problem would be to find out if your system is a 32-bit system if that's the case and you're trying to add more than 4 GB of RAM it will not work because you would need a 64-bit system to run anything higher than 4 GB.
If this helped awesome, if not just go ahead and let me know and i'll see what else it could be. Hope this helped man!