AC power adapter type cannot be determined

I have a 1 1/2-year-old Inspiron 6400 / E1505.  I recently started receiving the following error message on bootup:

The AC power adapter type cannot be determined.  Your system will operate slower and the battery will not charge.

 

Please connect a Dell 65W AC adapter or higher for best system operation.  To resolve this issue, try to reseat the power adapter.

Strike the F3 key (before the F1 or F2 key) if you do not want to see power warning messages again.

 

Strike the F1 key to continue, F2 to run the setup utility

Press F5 to run onboard diagnostics. 

I found the troubleshooting wizard on Dell's website that addressed this issue, and I carefully followed all the steps: checking for broken or bent pins, unplugging the power cord from the adapter, etc.  I also tried another power adapter from a friend's E1505, and it worked fine.

So, I believe the problem lies in my power adapter.  Do I have any options other than replacing the adapter?  I'm not afraid of soldering, and have done some electronics work, so if there's a part I can replace inside the adapter, I'm fine with trying that.  (Additionally, ever since I bought the computer the adapter has frequently made a "pop!" noise when I plug it into the wall, and occasionally I can see the spark as well.  I don't know if that is normal, but possibly it led to the adapter's partial failure.)

Thanks,

peppergrower