Op Amp buffer chain "latching"
1 - The fact that TP1 is at zero is a good sign. If you know how inverting amplifiers work, you should recognize this.
2 - Assuming that TP1 is actually connected to the output of the first AD820, that is indeed a problem. You should disconnect the resistor from the output of the first AD820 to the -input of the second, and see if the output of the first is actually stuck at zero.
If it is, either you have a bad op amp (unlikely, since the first op amp apparently had the same problem) or, more likely, you have accidentally shorted the output to ground.
3 - A draw of 40 mA is indeed significant. Your circuit as drawn cannot do that, so it's pretty certain that your schematic is not accurate and you have a pin connected to ground or power supply which should not be.
4 - A possible exception to 3 is the chance that your impedance levels and layout are causing either or both 820s to oscillate. I don't know how you've constructed your circuit, but it's possible that your 1 M input resistors are interacting with the input capacitance (caused by sloppy layout) and the result is oscillation.
As a rule of thumb, op amps should NEVER be operated without a feedback capacitor, especially with large input resistances. Try putting a 10 - 100 pF cap across each feedback resistor. With 1 M resistors, this will rather limit your available bandwidth, but that's better than oscillation. If this fixes the problem, you can experiment with reducing the capacitor values - but not until you've tried decent-sized caps.