Xperia X10 Mini/pro :: Randomly Shuts Off While Charging?

I purchased an X10 mini three days ago and I've had nothing but trouble. It took three hours to finally get it to recognize my SIM chip. Now when I connect to the charger (PC and wall socket), it'll start charging and the light will turn orange but it will spontaneously shut off. As has been pointed out elsewhere, the phone won't charge unless so it's on, so you can see how this is a problem. I haven't been able to get the battery to fully charge (the best I've gotten is to 75%) and it gives it still gives it's status as discharging when it's hooked up. To add insult to injury, once the phone shuts off, I need to repeatedly press the on button (sometimes in conjunction with the home button) to get it to turn on. I'll get a little vibration and then nothing happens. I need to try about a dozen times before it'll finally respond. Do I need to return the phone for being defective or is there something I can do? I've had SE phones for the last six years, but this is enough to make me switch to another brand.