Not charging, not coming on?

Alex, the logic board on your battery is actually what makes it a smart battery, it communicates with the power management IC. The logic board/circuit is part of the single-wire system which stores the battery code and tracks battery readings that typically include voltage, current, temperature and state-of-charge information. Batteries are much more than just a storage device. Anyhow, since you already did your voltage measurements, try to see what you get on your battery contacts when you plug the phone in. Remember that the end-of-discharge voltage for most Li-ion is 3.00V/cell. At this level, roughly 95 percent of the energy is depleted and it will continue to discharge very rapidly if the discharge were to continue. "To protect the battery from over-discharging, most devises prevent operation beyond the specified end-of-discharge voltage." I seem to remember that it is 2.7 volt for the iDevices. If the battery is depleted past that point, it will not charge. there is a way to "quick" charge, or wake up the charging circuit with a 9V battery. There you briefly attach the 9V to the same polarity contacts of the iPhone battery, and it may bump up the charging circuit. So, on a good circuit, I would expect to get a voltage measurement of anywhere from 3.8/4.0V-2.7V You can also try to charge it on an AC adapter. Check on here for the dock connector pinout, as well as some of the voltages that are expected. That way you can see if you have the right voltage coming to the phone.The attached image may just give you something else to measure ;-) So, to make a long story really short, I'd start of with a new battery....:-) Hope this helps, good luck.