No, you don`t connect them. Sounds like it`s either wired wrong or the dc socket is faulty. For clarification check that ground is wired to the lug that is connected to the centre pin, usually by a small rivet. Try connecting a new dc socket to your adapter without anything soldered to it, check the voltage, ground and 1 off the other pins will give you 9v, ground and the third pin should give you 0v. How it works is, ground is always connected, but the positives aren`t. When you plug in an adapter it provides power via the ground and 1 of the positive lugs but switches off the other lug so the battery isn`t connected at the same time. Sounds like you have the adapter wired up to the battery pin and your switching it off when you plug in the adapter.
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