BTC Treasure Hunt Volume 2
If it was between 2010-2011, it must have been MtGox [dead], Britcoin [dead], Bitmarket [dead], Bitstamp [alive], Kraken [alive]. If she's lucky, she used Bitstamp or Kraken.
She stored the BTC on the exchange or did she ever transfer any to a wallet?
If you know the company or individual who owns the domain her email was registered on, I'm sure they'd be willing to register her username (probably would need to add some motivation by way of money).
I don't know of any exchange that would accept giftcards to fund your account, so there must be something in her bank statement or credit card statement to reveal where her funds went.
Also did she use her legal name to register on the exchange?