I'm not really deep on Bitcoin, so this probably needs to be proofread....
Think of bitcoin as a ledger. Any time you get bitcoins (mining, giving bitcoins) the transaction goes in the ledger. "5000 BitC => wallet 0x748a53cb56" or whatever. There's fairly good crypto making sure it's a valid ledger ("mining" is actually you proving the crypto work to make it valid - you get paid in coins for validating the blockchain). There's no "unique file" per se. There's no single bitcoin.com/blockchain that everyone supports. You have a copy of it, and the crypto makes sure its the same as everyone elses. (interesting issue if the blockchain gets so big that its too big for mobile/embedded devices). There's some edge cases as far as timing (including the "transaction malleability" flaw) that mostly seem to be worked out, if you pay attention to Best Practices.
So, the ledger says you have 5000 BitC. When you put them in MtGox. You in effect hand this to the 'Bank'. They now have your BitC. Now, they do their thing - they made money on processing. Think like PayPal transaction charges more than any bank loans.
Now, something happens that takes away those bitcoins. Can be fraud, can be "transaction malleability" (but in this case, was unlikely to be that). Either way, their BitC stash is gone, meaning yours are gone too. Can you track them? Theoretically, since everyone can see the ledger. In theory i can track numbers or BitC moving in and out, but not "your" BitC.
So... you went from having 5000 BitC to "having nothing but trust" once you gave it to MtGox. You truly lost it, once MtGox had its wallet emptied, either internally by fraud or externally by attacks, because at that point there's zero value in that trust - the coins are gone. In some ways, i don't know how anyone gave their money to an exchange. There's no guarantee they'd ever pay you, either in BitC nor cash. The fact it worked as well as it did is a shock to me.