Is my controller shot? A little help.

[slaughinghouse]

I'm wondering if my controller battery is shot. I always let my controller's battery run completely out before recharging. Recently, it did just that, but now I can't get it to recharge. If I unplug it from the USB, the lights blink, but if I press the PS button it doesn't stop blinking and go to the single light. Once I plug it up to the USB again, it stops blinking and I can use it again.

I tried switching USB cables, but there doesn't seem to be a change in it holding a charge. I just want to be sure that it's the controller (which I think it is) and not the USB cable (which I don't think it is) that is the problem. I'm guessing that means it's time to buy a new controller, yes?

Thanks in advance for your help.