although you done a screenshot of your desktop computers wallet history.. do you also have a blockchain.info wallet aswell.

it might be that the funds were just swept into a new "change address" stored in a blockchain.info wallet. (thus not showing on your desktop computer)

if you have never copied your private keys into an online wallet service from your computer, then it is worth checking your computer.

think about where the private key of 1DMLBZE9GY.... came from.. did you import the key from another service. or was it generated by your desktop bitcoin program.

if from a service (paperwallet/blockchain.info/brainwallet) then that may be the source of loss.. if generated from your desktop program and never exported the address out to an online service. then the source of the loss is most definitely on your computer