You say that signals at IN- and IN+ come from the same source. That makes no sense in the context of the rest of this question, and the circuit you've shown us. This is a differential amplifier, and by applying the same signal where you've marked "4.5" and at the non-inverting input, the difference is zero, and regardless of the gain you set with R2 and R3, the output won't do what you expect.
If that's not how you've wired it up, then read on. I'll assume from this point onwards that the node marked "4.5" is a fixed +4.5V source, not some AC signal input.
If in the real circuit you have +4.5V output, then I am confident that your opamp is fine, and the input signal (at the non-inverting input) is also centered on +4.5V. With a gain of 2 (as you have it here) any fluctuation at the non-inverting input should be measurable at the output.
Barring any wiring errors, or other silly mistakes, the fact that you see no deviation from 4.5V in the output tells me that there is no AC component to the signal at the non-inverting input. In other words, the previous stage's output is stuck at +4.5V too.
If you really want to see if this stage is working, instead of attaching the input to another opamp source, first try manually applying +4.4V and +4.6V (using a potential divider, or potentiometer, perhaps) at your input, to verify that it's good. That way you isolate this particular stage, and you can rule out problems from elsewhere, like frequency or bias issues.