So your first problem is physical cabling - obviously.
To connect a Catalyst 2960 to two power sources, you need to leverage an ATS, or a Cisco external Redundant Power System.
I will never buy another RPS again - ever.
They are the root of all evil in this world.
I bet you can find them on eBay for dirt-cheap as most people I know will practically pay to get them removed from their sight.