Weird.
If the computer is OFF, you should have been alright. Yeah, it's safer to unplug, but I've replaced a lot of graphics cards into pc's that were plugged in but not powered up and not had a problem.
This does not mean that you should do it... it just means that if something bad happened it was darned unlucky.
Static, on the other hand can DEFINITELY zap both cards and can also cause cards to work and then stop working. It used to be that everyone was recommended to have a static strap when working on anything inside a computer.
Now the recommended practice is to ground yourself to the metal chassis of the pc.
It really sounds like maybe something isn't making good connection in the socket. It is possible to crack the plastic socket while removing the old card. Then it won't hold a graphics card properly anymore.
I'm also wondering if your power supply has enough power for the different card.
So... test the original graphics card. Make sure it plugs in securely. If it uses an extra power plug, make sure THAT is plugged in securely. See if you can get the computer to boot in the original configuration.
Then pull the old graphics card and plug in the newer one. Again, make sure it's seated properly and if it needs power make sure that it's power plug is seated properly. See if you can get it to boot.
If the newer card is stopping working you might need a better power supply to supply power to it. You might also just have a card that is bad... it happens. You might be able to get it replaced under warranty.
Good luck and post what you find back to the board so that others can see what you figured out.
Good luck!