What would ideally happen is he'd keep paying his share.
What will realistically happen is a weird game of chicken. He doesn't want to pay and knows you don't want to get evicted. He's probably not going to pay, knowing that rent is an all or nothing payment. He'll count on your desire not to be evicted to help ensure the full payment gets made.
Your landlord isn't going to accept partial rent, and they're not going to particularly care why it's not a complete payment. The landlord will evict all of you for non-payment if you don't figure it out. It sucks, but that's how it'll probably go down.
As for the other issues, your roommate is entitled to take his personal property with him, including the internet box. While the lease may say power has to be in a leaseholder's name, it doesn't say which one or that it can't change. The power company 100% does not care if he shuts off power in his name. Your landlord may care when they get the bill, though. Best to get it back on soon...