The only sensible action you took was blocking the offender.
What to do if they don't resign
Start another game with someone else..and make him wait the full time period before you move,leaving your name on his game cache..for months hopefully.
Promote all your pawns to Queens. Each time you do, throw away the Queen, until you just have one left. Then keep making worthless moves, avoiding stalemates or three-turn repetitions, and see if you can win on time.
They probably play on because you wont mate them, and you play on cause they wont resign. It's an odd predicament.
resigning from a game is that players chioce, even if you know for certain that they are beaten if they do not resign you should keep playing until checkmate. if you cant mate them then the game was not won by you for certain in the first place." 1) Resign yourself! Give them a hollow victory. I tried this a few hours ago and the guy offered me a rematch! I guess he didn't get it." He probs thought you were an idiot for resigning when you were winning and thought he score some easy rating points by playing you again.
"2) Have fun. I had a knight & three pawns vs. a lone king. I knighted all of my pawns." and still you didnt checkmate " ? why ?
"In both cases I blocked the players from further games." why would they want to play you again would be my question also when you werent as good as you apparently are did any one block you for not knowing when you were beaten my guess is no ?
Throw away the Queen? Is It allowed to throw away pieces during the game?
I meant, by putting the Queens right next to their King so they can take them.
When you have an overwhelming game against someone who won't resign you can do whatever you want, so have fun! You should probably make sure you win, failure to win will only encourage them. Award yourself bonus points if they resign.
They probably play on because you wont mate them, and you play on cause they wont resign. It's an odd predicament.
i'm sure Bill Hartston could write a bestseller from this!
Normally, it they do not resign, you have the right to kill them. I remember this from my army days.
Is very common that player don't resign ,so You need be prepared to beat they on the board,What is the matter to continue playing? The chess game has multiple ways to win.
maybe you could say you have a terminal illness and only have 30 seconds to live and resigning the game would enable you to die with a smile on your face ?
it worked for me in 4 out of 5 games when my opponent refused to resign on the "you must resign" move number.

First check the times, maybe they are hoping for a time forfiet.
If time if OK, then a couple of ideas:
1) Resign yourself! Give them a hollow victory. I tried this a few hours ago and the guy offered me a rematch! I guess he didn't get it.
2) Have fun. I had a knight & three pawns vs. a lone king. I knighted all of my pawns.
In both cases I blocked the players from further games.