Snapchat, like many other similar applications, uses the phone number to activate the account. Your iPad needs to have 3G connection to insert a replacement SIM with the old number to access the account. If you are on a contract with the carrier number, then request a new SIM card with the old number. They should issue one. After this, register again using the standard method, and since you already have an account, use the link below to reset the password, then go back and log in.
Additionally, you can reset the password to your old account using the following link: https://accounts.snapchat.com/accounts/password_reset_request