so
Dragging out online games just for spite

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So...it's freaking retarded and should be dealt with by Chess.com staff.
Inb4 someone spews the "player's rights, player's rights" "you agreed to the time, you agreed to the time" BS.
Some behavior should be dealt with.

Everybody only has a certain amount of vacation time: if this person is expending their vacation time to drag out a game, that's less time they'll have to do it again. It's an exercise in patience.
It's also something some people use when they think their opponent is cheating - they report the game and try to drag it out in the hopes that their opponent will be banned before they lose that game. It's one way to use your vacation time as well.

Everybody only has a certain amount of vacation time: if this person is expending their vacation time to drag out a game, that's less time they'll have to do it again. It's an exercise in patience.
It's also something some people use when they think their opponent is cheating - they report the game and try to drag it out in the hopes that their opponent will be banned before they lose that game. It's one way to use your vacation time as well.
I wish someone would accuse me of cheating. It would be the best compliment of all time ;)
I am not really talking about vacation time. I am talking about people in positions like this...
Dragging the game out to the bitter end, letting the entire time between each move (1 day, 3 day, 7 day) pass before making the next move. It would take another 10-20 moves to achieve mate. So we are talking weeks or even months! Funnily enough, getting to that position only took 2 days.
your solution is no good though. The staff probably is not big enough to sit around solving these problems all day.
It could be automated, however, with some thought. Still, consider... ALL the solutions that exist to this problem are unsporting. Granted, your opponent is also being unsporting, but 2 wrongs don't make the sport better. You are basically telling someone that they have lost and to accept this whether they see it or not, which is simply not how chess is played.
I agree with you, it is annoying, but I question that there is a "good" way to fix it.
My solution is to play shorter games, move once a day, or at most, 2 days per. Those 5 and 7 day between moves are just ripe for abuse of this sort.

If they take less than three days -they are not breaking any rules and myabe you were a jerk earlier in the game and they are just giving you payback.I dont need more rules for chess.

Ah, okay, that's different.
I don't think staff can or even should intervene in this case - there's still the possibility you might mess it up and get into a stalemate or hang the pawn, particularly if you get careless or impatient.
One thing that might help is Conditional moves - you might have to define eight conditions to cater for all of the possibilities, but then your move executes straight away and don't have to think about it until next time. It doesn't make the game go much quicker overall, but it does mean you don't have to spend as much time & energy thinking about it.
Unfortunately, it's not practical to define the conditions more than one move ahead, since the work involved outweighs the benefits, but I've found that it helps. It works even better if you can cut down on your opponent's options so that you can define the conditions further ahead.

I do slow down when I suspect my opponent is cheating. Won two games this way - my opponents' accounts got closed before I got mated. Lost a game where after-the-fact my opponent's account got closed. Makes me think in a lost position the thing to do his not resign and move as slowly as possible.

I agree that it is rude and quite cowardly to stretch out a lost game as long as you possibly can. However, there is nothing you can do about it besides refusing to play 14-days-per-move games. After all, your opponent has 3 whole days (or whatever) to make his/her move, and so do you. If they want to spend that whole time trying to find the only legal move, they are free to do so.
My advice on the matter is to block your opponent after the game, or simply make a note of the member and refuse to play with him/her again.

You can also check out the other games they might have in progress - I was a little annoyed that one of my opponents was using the full allotment of his time in a game he was way down on, but when I saw he had some ridiculous number of games going at once (something like 80+), I could understand why he was only getting to each one as the time duration came up.
Has anyone ever experienced an opponent that, once they have lost, let the time go all the way down to just a few minutes before making their move? I think that's pretty crappy, and it's more common than you might think. They play their moves normally, but when you have won (such as in a king and pawn endgame) they use up all their days in between each move and drag it out a month or more.
This technique can also be used to artifically inflate someone's rating. You pile up your wins and drag out your losses. It works like an insurance company (far more coming in than going out).
Personally, I think Chess.com mods ought to have a service for premium members where you can send them the link to your game and have the win awarded.