The offset null pins of the LM741CN op amp don't seem to work properly
Figure 1. The original circuit.
You are running the op-amp from a single supply and have the inputs tied to ground. You can't. The inputs must be a few volts above the negative rail. You need to supply a negative voltage on pin 4.

Edit after question updated.

Figure 2. The modified circuit.
This is better and you should see some ability to modify the output voltage. Note that you have a gain of 1M/1k = 1000 which is very ambitious for a 741. Try a gain of ten or twenty and continue your experimentation.