Just a thought but have you tried to reset your Nuvi after :
Disconnect the Nuvi from external power.
Flip up the GPS antenna
Press the Reset button
Connect the Nuvi to a power source. It should now automatically turn back on.
I am sure you double checked your work for any loose cables and check the troubleshooting guide [http://www.ifixit.com/Wiki/Garmin_Nuvi_680_Troubleshooting#Section_Bad_display|on here] and just in case you need it, [guide|4713|here is the guide]. Hope this helps to get you started. Good Luck