A 2FA Electrum wallet is just a fancy MultiSig 2of3 wallet. The only way to get the coins out is by having the 2 of the 3 private keys required to be able to sign a transaction to move the coins...
1 set of private keys is owned/controlled by TrustedCoin, but they'll only sign it if you have the GAuth token... Which apparently you've lost.
The other 2 sets of private keys are generated from your seed... By default, it only stores 1 set of private keys in your wallet (and you send to TrustedCoin to use their set to countersign)
When you restore from seed, you get the option to "disable" 2FA which restores both sets of private keys into your wallet, so then you don't need to send to TrustedCoin.
The only way to recover a 2FA wallet is with the seed... So if you have no seed and/or no GAuth then your coins are effectively locked in.