The "brown and abnormal" look around your power jack might be from two things. Either Dell replaced your power jack (hence your new power adapter) or your new power adapter has burnt out your connection. Sometimes adding solder might help but that is only a short term solution.
Here is an insert from a Wiki page that might help you, if you are using an Inspiron.
Dell Inspiron - Wikipedia, the free encyclopedia
Most Dell laptop computers have a special external power supply (PSU) which cannot be replaced by a third-party universal supply. The PSU has a chip which produces a special signal identifying the PSU as by Dell and specifying its power, and a special 3-pin connector (minus, plus, and ID). If a power supply not made by Dell is used, and the cable near the connector becomes damaged as is not infrequent after some use, the battery stops charging and the CPU runs slower, although the computer can be used indefinitely so long as it remains plugged in. If this problem is present at startup the message "The AC power adapter type cannot be determined. Your system will operate slower and the battery will not charge" is displayed. This will continue until the external PSU is replaced. A few third-party suppliers make power supplies with specific provision for Dell computers at lower prices than Dell's. It is possible to work round the slowdown, but not the battery charging, by installing a CPU clock utility.[18] On some models (the 9100 for instance), the problem can be worked around by starting the computer without a battery installed and fitting the battery after the computer has booted.
Here is an insert from a Wiki page that might help you, if you are using an Inspiron.
Dell Inspiron - Wikipedia, the free encyclopedia
Most Dell laptop computers have a special external power supply (PSU) which cannot be replaced by a third-party universal supply. The PSU has a chip which produces a special signal identifying the PSU as by Dell and specifying its power, and a special 3-pin connector (minus, plus, and ID). If a power supply not made by Dell is used, and the cable near the connector becomes damaged as is not infrequent after some use, the battery stops charging and the CPU runs slower, although the computer can be used indefinitely so long as it remains plugged in. If this problem is present at startup the message "The AC power adapter type cannot be determined. Your system will operate slower and the battery will not charge" is displayed. This will continue until the external PSU is replaced. A few third-party suppliers make power supplies with specific provision for Dell computers at lower prices than Dell's. It is possible to work round the slowdown, but not the battery charging, by installing a CPU clock utility.[18] On some models (the 9100 for instance), the problem can be worked around by starting the computer without a battery installed and fitting the battery after the computer has booted.
