Phone won't turn on at all. Voltage problem?

I bought a Nexus 5 which was described as non-functional. The battery life was getting shorter and shorter until it died and did not turn on again.

I changed the battery and checked if it gets charged at all (with a voltmeter). The voltage was about 2.4V, but it got charged. I read about 3V after a while on the charger. Even when it reached 3.6V the phone would not turn on. Will the phone only turn on, when it has 3.8V? It's on the charger for some time now, will check the voltage again soon.

Any ideas what else might be the problem? I have replacement parts lying around, already changed the charging module, but did show the same results.