Simple Non-Inverting Op-Amp Problem
You need to connect the battery (-) to GND in the first diagram, and the battery (+) to ground in the second. 

But before you do that, increase those feedback resistors by several orders of magnitude. 10K to 100K for the MCP618. You must not exceed the absolute maximum 2mA input current, and the second circuit will pass around 7mA into the inverting input until the output catches up with it. The first circuit also could pass a significant current under certain conditions (with power supply voltage = 0), so you can add 10K in series with the non-inverting input (on the output of the batter). Such relatively high value resistors will protect the op-amp inputs and from latch-up. 

You don't need (and shouldn't have) a resistor in the supply rail. A bypass capacitor of 100nF or so across the supply rails would be good.