The problem isn't SOL (since your browser will likely remember your password anyway), the problem are all those websites you haven't visited for a long time. When you finally decide 'I need something from them, I guess I'd better log in', you likely won't be able to, since you often sign in using a combination of email & password, and if you haven't been active for a long time, they'll 'confirm' you are who you say you are by sending an email to the dead account—meaning your entire history of services, credits and purchases with the company are toast!
It's time to review those old account, and you can go ahead and purge those accounts you haven't used for a long time so once you get get a new internet provider, you can start fresh.
The other option, is to simply continue paying your current internet bill (after dropping any extras you're paying for, so you're only paying for basic minimal service) and then when you have a new provider, then switch over all of your accounts while you can still rely on the older address. Frankly, this is so common, I'm continually amazed that internet providers don't offer a 'carry over' services, where you pay a minimal fee to keep your email alive until you can transfer everything. But Corporations don't do what people need, they're only focused on ever growing profits. :(