Will my phone charge if i plug the usb cable to my computer?

I have a Galaxy S Fascinate. The charger is also a usb cable. Right now i'm having trouble charging my phone for some reason. Am i able to connect the usb cable into my pc and use it as the alternate charger or no?
****Right now it's not charging at all even though it's i plugged it to the charger. Does this mean the charger ((wire)) is broken??
 
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