Non inverting op amp issue
Is there an impedance issue that I'm not aware of 


There is a difference in input impedance between the two circuits.

The input impedance of the non-inverting configuration is essentially the input impedance of the op-amp itself; that is, very high.

The input impedance of the inverting configuration is very close to \$R_{in}\$, because the summing node (negative input terminal of the op-amp) is a virtual ground. Another way to look at this is that the feedback will try to operate so that the input current is \$V_{in}/R_{in}\$ and your signal source will need to be able to supply this current.

But

But that is probably not your problem. Notice that the LM3900 does not have a typical op-amp input stage:



With those base-emitter junctions from the inputs to ground, you really need to operate this amplifier with the input terminals held near ground. Your non-inverting amplifier circuit doesn't do that, so it's not likely to work well.