My iPhone 4 will not charge, but powers on when plugged in. Suggestions?

Yesterday, my phone charged just fine and now, it's as if my charger cable has become Google. As stated in the title, it doesn't charge, but after I turn it off and plug it in, my phone powers on normally. So, I'm hoping to get some suggestions as opposed to my last resort: Buying a brand new, over-priced charger that will stop working only after a month and a half just as my current one has.

I'm assuming that the problem is my charger cable because I've tested it on other iPhones and got the same result.