"I split your post from the original post to which you attached since your problem seems to be different.
I am not aware of ICs that were misprocessed and that resulted in 0V output. However, I do know that the small 2x2 QFN requires special care when soldering or the IC will be damaged internally. The app note at http://focus.ti.com/lit/an/slua271a/slua271a.pdf explains the problem. Essentially, if the IC is heated assyemtrically, then the package and internal bond wires may crack and cause the IC to stop functioning properly. If you are absolutely certain that this is not the problem, then please send a schematic for me to review. If the schematic looks reasonable, then I likely will not be able to help further, since the ICs are non-functional, and the next step would be for you to return the ICs to your distributor."
There is no easy way to confirm the solder damage on the bench. You could try measuring each IC pin's resistance to ground and compare to a working IC (both out of circuit) but the pins on good ICs are very high impedance anyway so you might not measure a difference. The only way to confirm this type of soldering damage is through an X-ray of the IC. That is performed by our failure analysis team, once the ICs have been returned back through the original channel of purchase. If the any pin other GND measures as a short to GND, that would be another problem.
Do you have access to a hot plate, solder reflow station or oven?
I looked in our return tracking system and did not see any returns related to your specific lot code.
The A version is the same silicon as the non-A, just with the EasyScale interface disabled via EEPROM. But if you got the new TPS61161 non-A's to work, then soldering likely isn't your problem and you, unfortunately, got some bad ICs. As I mentioned above, I didn't see any returns related to your specifc lot code in our quality tracking system.
Can you tell me from whom you purchased them so that I get that bad lot removed from stock?