Is it my hard drive?

Please excuse my ignorance, I've never been very tech savvy. Anyway, I own a macbook unibody model a1342 which I bought refurbished from Apple last year. About a month ago, my little girl stepped on it shattering the screen. I replaced the screen just today, all seemed to go well, when I randomly got an error that read "Please restart your computer" - I did this, and everything seemed fine. I later reinstalled iTunes, and upon the reboot required, my computer refused to start up. I was stuck in the opening grey screen with the apple logo and circular loading icon. Then, it powered down. Now each time I go to turn on the computer, it sits in the grey screen for a while and immediately powers itself down.

I learned from these forums that the error message I got is a "kernal panic" (not implying that I know what this means, by the way, lol) and that what I'm experiencing is likely a failed hard drive. Is this true? What would be the next step for me to take? Would it be wise to buy a new hard drive and go from there?

Responses would be greatly appreciated as I need this computer for school.