Just verifying that the laptop will not work with the AC adapter connected and the battery removed, is this correct?
It may be that the DC-In jack is faulty and not that you have a problem further into the motherboard.
Here is a link to the owner manual for your laptop.
Scroll to p.21 to view the necessary pre-requisite steps and then the procedure to remove/replace the power connector, (DC-In jack).
You are fortunate that this is a plug in module so if it is faulty it is easy to replace, no soldering required. (use an Ohmmeter to test if it is OK out of circuit)
Here is a link to just one supplier of the part. It is not a recommendation to use them. It is shown to give an idea of the cost of the part. There are other suppliers online that may suit you better. Just search for Dell Precision M3800 Dc-In jack part for results