So, in this case, how do I claim victory?

What case?

claim what? show a game or number

offer a draw, or resign by choice.
you can't claim a win

unless it because time has expired

 my opponent left the game, beaten but not over, and when i see him on line, and hit resume, he declines to finish...the victory, in this case, was overwhelming, and the disconnect was obviously a technical play to avoid a defeat...apparently all you have to do, if you're behind or think you're beat, is to leave the web site, suspending the game in eternal purgatory

There are multiple threads about this.

The help file entry for adjournment. "If the game is not finished in 7 days, the game will be adjudicated by Chess.com. ". If this is still the policy, there may be too many for staff to handle.

Hi,

I'm new ti this site , and already played two games . Both the games, in between ( I was doing well ) , displayed the opponent has won the game . First one it was 5 min game , so I thought the time was about to finish ( didn't finish) and so , for the second game I didn't prest anytime . It started 10 min . Could you please tell what have beem the cause for my problem .

yes