I've not used cable for the internet (have DSL) so I can't speak for that side but I know that with my DSL connection, I have to provide a user name & password when I connect.
Yes, teens can be ingenious - deviously so - but with a little diligence you can set up a decent password that will be uncrackable by most teens.
I don't agree with NewBudda with regard to "reasoning" with teens. You're not really reasoning with them, you're negotiating. Watch Maury Povich, Sally Jessie Rafael, etc. to see what "negotiating with kids" gets you . If it were me and my only option was to lock the modem away, I'd TELL my teens (yes, I've had 2 of them) that I'd be checking the system to see where they've been on the PC. ANY breach of the rules will result in a complete lockdown of internet privelages.
There's always a better way. The fun is trying to find it!