I did the same thing once with a debit card / bank account that I closed 2 years ago and my account was stolen from me, so I contacted steam and they gave me a list of stuff I can do in order to get my steam account back.
What you need to do is get your parents to call there back and request a transaction report for the time you think the purchase was made, banks keep 5 years worth of transaction history, and send this information. (Highlighted in blue)
Immediately Contact Steam Support about the lost account
Provide the following information:
Steam account name
The original contact e-mail for the account
Select “Account Questions” as the category and “lost accountt” as the subcategory.
Proof of purchase for the account as outlined below:
If retail software is registered to the account, attach a digital photo or scan of the CD Key registered to the account. Write the Steam account username on the quick reference card or CD Key sticker below the code in permanent ink.
Examples:
If a game was purchased through Steam with a credit card, please provide the following:
The Card Type (Visa, MasterCard, Discover, American Express)
Full Name on the Card
Expiration Date
The last four digits of the credit card number - Do not provide the full credit card number
If a game was purchased through Steam using a PayPal account, please provide:
The Billing Name on the PayPal Account
The full Billing Address on the PayPal Account
The PayPal PayerID
The Invoice ID and the Transaction ID
If any other type of payment was used, please explain this in the support ticket.
Good Luck.