My Dell D 600 will not charge the battery and a message appears at start up that says Ac adapter not recognized What do I need to do to get my computer to charge the battery

The adapter could be faulty or has failed slightly and is below the operating limits. This means you probably need to replace the power adapter.

update system bios

As you say the system is 4 years old update the bios
your download link is here!
IMP. Be sure to plug in the battery and it should be charges above 10 % and the system should be connected to the mains power supply also ensure there will not be a power outage during the update process
this will resolve the issue 100 %
Dont forget to say thanks!

run system diagnosis with dell cd. it will start when u boot ur dell 2650 with driver & diagnosis cd

If a new DELL ac adapter (3rd party Adapters are not recognized and the charging circuit is disabled) and a new battery doesn't resolve then the charging circuit on the motherboard is bad

When you received the system as out of the box and you get this message "The AC power adapter wattage and type cannot be determind" let the Dell tech service know that they sent you a wrong or incorrect type of AC Adapter.
If this message not was not appearing before it just happened recently try to download and install the latest BIOS version from the support site.
If all fails remove the batt and check if laptop can work with AC adapter alone, because issues like AC not determine may not charge the battery and laptop may not work with AC as well, maybe laptop is already running on battery power.

-check the system battery information and charger information of the computer; restart the computer, while the computer is booting up, press F2 repeatedly; check "battery info"
-if it stated ac adapter = unknown device ; update the BIOS (-visit support.dell.com
NOTE:other computers may have different BIOS, if it is not the same you may have to consult manufacturer
-click on drivers and downloads
-click or choose by service tag
-download the BIOS and install it on the computer)
-check information after updating; if same message AC adapter = unknown device; call manufaturer for a replacement AC adapter, if status has changed it is a battery problem or motherboard, contact manufacturer to test battery

the Dell AC adapter has a sensing pin so the bios can determine the wattage of the adapter. If the system cannot ID the adapter, the battery charger circuit is disabled. You'll need a functional DELL ac adapter to get the battery to charge

If you don't get any errors when you startup on battery then all you have to do is call Dell. Get work order number and send them the laptop and adapter. They are very fast. I sent a laptop to them last month and I had it back in 3 days! I was surprised.

The Dell 1501 ac adapter (possibly other Dell’s as well) has been known to be problematic because of its lack of a plug to jack secure fit. You will notice that the plug can all too easily be pulled from the jack, as opposed to other systems where the plug fits more securely onto the jack. The plug and jack combination is poorly designed so that over time, the plug will come unseated depending on how much movement the machine is subjected to. This will result in power error messages or outright power-up failure. So before assuming you have a faulty adapter, make sure that it is not just a loose plug that is causing the problem. If you look inside the jack, you will notice that there is a 3mm region of non-conductive material nearest the surface of the jack. Use a strip of standard electrical tape 3mm wide and long enough and wrap it around the base of the plug (you may need more than one layer of tape to get a good fit). I have used this method to secure my plug and it has served me well. If the tape comes undone over time, just simply replace it. A more “elegant” method would be to use an “O” ring of the appropriate size (about 6mm) around the base of the plug in lieu of the tape.