If Blockchain support are not able to help you and you have the 12-word “backup phrase” I believe the best course of action is to migrate to a new wallet.
By migrate wallets I mean use your backup phrase with wallet software written by a different organisation. The only important thing stored in a wallet is the private key generated from the backup phrase (also referred to as a seed phrase or recovery phrase). So any wallet that contains that key can be used to spend money that has been received at addresses created from that key.
If you are a frequent user of Blockchain’s other services, such as buying and selling Bitcoin or other cryptocurrency trading, you might not want to do this. However there are alternative exchanges that you could use instead.
There are several wallets that have a much better reputation than the Blockchain wallets.
For example see …
As well as the backup phrase, you need to know the “derivation path” for your old wallet. The accepted answer to the linked question assumes a derivation path of m/44'/0'/0'/0.
Instead of importing the key to a new type of wallet, it can be safer to sweep the keys into a new type of wallet. Sweeping just means using the old key in a new wallet to create a Bitcoin transaction that transfers the money to the control of a new key in the new wallet. If you ever imported additional private-keys into the old wallet you’d also have to either repeat that and import those extra keys to the new wallet or instead sweep those keys into the new wallet. Given your situation I would not sweep any keys at all until certain of the derivation path of your old wallet, it would be safest to first try importing the keys using the backup phrase and, once everything is working, then move the money to new keys.
If all this seems too complicated, you might reasonably conclude that Bitcoin is not for you.
