Hey David,
Ok, first, there is nothing particularly fancy about the circuit. It is using the dual comparator (LM393) to test the charge state. There are A LOT of smd passive components on the copper side, more than I would think requisite and yet there they are....there are also what appear to be 2 smd active components on the copper side. They differ in appearance from the passive components in that they have 3 leads instead of 2. They are located near the transformer secondary on the copper side. If you can get a number off them, please do. Also, if there are any other SMD components with three or more leads, please report their location and any markings on them.
Visually the only thing I note is the 100ohm current resistor shows some small signs of over-heating. It is difficult to guess if perhaps the resistor is out of tolerance, I wouldn't guess so, but that would be the first thing I would test.
I assume you are in the UK as the charger was made for the UK market. This being the case, before we get too far into this, remember this is an option:
http://www.battery-discount.com/Bat...r-compatible-with-DEWALT-ref-type-DE9103.html ; just saying......
Ok, how you proceed from here depends a lot on what equipment // skills you have. I don't see anything proprietary on the PCB, so the easiest solution is likely the "shotgun" approach; that is, start replacing components until it works....If you have a Multimeter, we can do some fairly quick testing of the resistors to ensure they are within tolerance. As previously stated, the only "tell-tale sign" I see is the slight discoloration of the 100 ohm current limit/sense resistor (brown /black/brown). Test it first, or simply replace it if you have one on hand.
The next thing to test (I assume you have a Voltage meter from post #8) is the voltage on all three pins of the "P19Nx" device with respect to ground in all three cases ===> 1) No Battery 2) Battery w/Charge 3) Dead Battery. In reporting this info, assume Pin 1 is to the left when viewing the device from the side with the writing.
Example: No Battery: Pin 1 = 17Vdc Pin 2 = 0Vdc Pin 3 = 5.1Vdc
While the part# P19N did not yield any search results, it is quite possible it is in fact a 7805 or some other voltage regulator (though it could just as easily be a transistor//mosfet).
In addition to the info about the non-passive smd components, and the voltage on the pins of the P19Nx, it might be a good time to let me know what skills//tools/experience you have and if there is a local electronics components vendor. If you have no tools and self-describe as "little or no experience with electronics" I would urge you to consider the £ 44,90 option simply because this project could easily become a time sucking vortex that ends in failure. You should also be aware that a NiCad/NiMh battery that reads 0V is quite frequently permanently damaged. All that being said, I also need to disclose that I am NOT a trained technician, but rather a self-taught amateur with a good track-record, but PLENTY of failures to go along with the successes. I would hope that some of the professionals here would correct me if I suggest something too far out-of-bounds, but you will need to proceed with the understanding this could end in failure.
Fish