In any case, if you have not touched your wallet for 7 years, it will not sync If your electrum version is older than V3.0.5, you will need to update the wallet.
Keep your old phone working without touching it, download the wallet to a new phone, verify the signature, and since the Google Authenticator setup was at the software level (meaning your wallet is not Electrum 2fa with TrustedCoin (2-of-3 multi-sig)), then you can easliy recovering your wallet via the seed.
In new wallet click on Create / Restore a wallet, give it a name, enter your seed and will store your funds.
Thanks for the detailed breakdown.
So it looks like I need the enter the seed no matter what, right? That sucks!
Is there really no way I can update the Google Authenticator app, then install the latest version of Electrum, place my wallet.dat file on my computer, and then use the Google Authenticator 2FA token to send the money?
Also, just to be 100% sure (sorry if it's a stupid question), but when you say download the wallet to a new phone, this can also be done on a laptop right?
I can install Electrum to my computer, verify the signature, and then restore the wallet via seed there.
You just import the wallet on a new device and you already have the seeds will give you complete access to your wallet and the information in the new device as well, so once you done that then update whatever you want and restore the wallet on updated device and continue using 2FA or just opt for better password combination.
Placing the wallet.dat file of Electrum on other device will only work if it's not password protected wallet.