Hi Michelle -- Whoa! What happened to that poor penny? It looks so sad ...
There are two possibilities for a coin that looks like yours.
First, it could be post-mint damage, that is, mutilation that happened after the coin left the mint. PMD has no value, so, if your coin was damaged after it left the mint, it has no value.
Second, it could be a "struck through" error coin. Error coins that are "struck through" have value to collectors, because the error happened at the mint, not afterwards. It appears that your coin may be "struck through cloth." If so, a heavy piece of cloth got stuck in the minting machine and the two hard-metal dies came together with high force to create a "struck through" cent. If this is the case, my guess at value is $20 to $50 US dollars.
I am not qualified to distinguish which type of coin you have. Is it PMD, or "struck through cloth?" An expert who can tell you is Mike Byers. He literally wrote the book on minting errors. I suggest you contact Mike and ask for his determination and value estimate. He is an excellent numismatist, and he will surely help you. Contact him through his web site:
Here is a "struck through cloth" error coin which sold on eBay for $15:
For more "struck through" info, see these pages: