This can be caused by a number of things, so there's a few steps to take to cehck everything.
First of all, please check your system time and date. If this is set incorrectly, this error can manifest.
This can often occur after system changes have been made, or if the computer has been moved recently (If the motherboard battery has an issue).
If the problem persists, please try flushing your DNS cache. To do this, open the command prompt (press the Windows Key and R and enter: cmd) and put in the following command: ipconfig /flushdns.
In case this also has no effect, please download and run a copy of the game setup file (available [uel=www.swtor.com/download]here[/url]) and choose to reinstall the game. Don't worry, it's a fast process, and will use the existing good assets on your machine.
I hope this helps.
Thank you for the quick reply. I've verified my timezone settings and flushed the DNS cache, but that didn't solve the problem. I also uninstalled the game, and tried to re-install (I don't mind patching again if it means it will solve any future issues), but once the launcher opens, I still receive the message "login service unavailable."