Your battery will be around 3.8V and the charge port will be 5V if connected to a USB port or you Apple MFi-certified charging brick. If you are reading 0.7V, you are either not probing the right place or have a defective charge port. Check you charging cable, brick to see what voltages you get.
At this point, your battery is discharged and will read a much lower voltage. Ideally, if you can replace it with a known-good battery or try and charge it in another device.
If you have eliminated the battery and the charge port, then you likely have a charging circuit problem on you logic board, specifically, your Tristar IC (U2) is probably bad. No-charge or fake-charging are classic symptoms and can occur if you drop the phone or use low quality charging bricks.
If the Tristar IC is the problem, this will not be a DIY repair unless you have experience doing micro-soldering.