Re: Galaxy S4 will not turn on or Charge- only blue light blinking
If the battery drained really low (you normally can't drain it to totally flat - the phone will shut off somewhere around 5%), it won't be charging for about the first hour, it'll be in ramp-up - kind of a preparatory step to charging. Just leave it on the charger and if the battery isn't totally shot (and I've seen batteries that had so little voltage that on the voltage vs. State of Charge curve [which is how the SoC is calculated] they would have registered about -200%. I just looked at a phone on the bench with a battery that came in like that and it's been sitting - not in the phone - at 100% for about 2 weeks, which tells me that it's a good battery. Most batteries will self-discharge enough in that time to show about 99%. ["Just looked", because I had to put the battery in the phone and turn it on to put that info in the post.])
If the battery won't show any charge at all after 24 hours, and we know that the charger is connected to the phone and the charger is supplying power to the phone (the light is on), either the battery is totally gone (you can get an Anker - good battery - for $10 from Amazon) or there's something wrong with the phone, and that would take a repair shop to diagnose.
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