Why won't my phone charge or turn on?

Okay so my battery has been working great and I haven't had any problems with my phone previously. I plug my phone into my charger at night when the battery was nearly empty.

The next morning I woke up and my phone had no battery and would try to turn on but wouldn't. I plugged my phone into the wall and it won't charge past the red screen with the lightning bolt.

I tried using my dad's charger (which I know works) and it didn't do anything. I also tried doing a hard reset (holding the power and home button) that didn't work either.

Next I tried putting my dad's 4s battery in to test, but it was the wrong connector.

I measured the voltage of my battery with a volt meter and it read 3.5 volts out of 3.7...

I also tried plugging the phone into the wall without the battery in it and I noticed that the phone will turn on and come to a screen where you can make an emergency call, but you can't do anything else and will otherwise tell you to connect to itunes.

Next I tried putting the phone in to DFU mode and doing a restore to factory settings and had no luck.

Not sure if this is related to the problem or not, but my dad's phone was plugged into my charger after I had this problem and it had 100 percent battery before I went to bed and in the morning it had only 20 percent.

I have no idea what the problem is...I'm hoping its just the battery, but I won't be able to test that until monday. I've done a lot of researching online for this problem and haven't found any definite results