New non-Dell AC power adapter won't charge battery

I have an old Inspiron 8600. The original AC power adapter finally died. The cord had been bent and there were bare wires that couldn't be taped together any longer. I bought a non-Dell AC power adapter, as it was the fastest fix and Dell won't allow returns of its "opened" products. My laptop recognizes the AC power adapter, but now the battery will not charge and is completely dead. Windows notes the computer is running on "AC power". I was not having any battery problems before this, so I think that it's an issue with the AC power adapter, but I don't want to spend $70 on a Dell AC power adapter that is non-returnable if it won't solve the problem.