IPhone 4 :: Suddenly Died - Will Not Hold Charge (won't Call / Text Or Get Internet)

My iphone 4 suddenly died last night even though it said it had about 40% power. When I plug it in, it turns back on but will not connect to anything (no internet, and I can't call or text). As soon as I unlpug it, it turns off, and sometimes when it is plugged in it either says it has 0% or 100% charge. After about 60 seconds of being plugged in it turns off and restarts. It won't start up fully when I plug it into my computer, it just shows the Apple symbol before shutting off again. I am thinking this is a hardware issue. Is it possible that the battery is so drained (since it won't hold charge), even when it is plugged in, that it doesn't even have the power to connect to the internet or call or anything? I have had this phone for about 1.5 years.Â

Important note: I had it fixed about 2-3 weeks ago when the whole front piece of the phone was shattered when it was run over by a car, lol. Even in that state, the phone continued to vibrate when recieving calls, and when the front piece and home button were replaced everything was working except for the camera. Maybe some internal damage is just now catching up to the phone?

Info:
iPhone 4