Jack -
Yes, there is a better converter, available as an easy retrofit if you choose to do the job at some time in the future. But that is not the problem you are experiencing now. Like the others, I suspect that the main battery fuse is gone, which means that the battery cannot supply power to the TM, and cannot accept charge current from the charger in the converter.
In 2002 models, the main battery fuse was a glass cylindrical fuse with metal end caps, and the in-line fuseholder was located about 6 inches from the battery's positive post. The fuseholder was white nylon, which twists apart into two pieces. If this is the one you have, look to see if the ends of the fuseholder have turned brown. This indicates overheating of the fuseholder, and was a fairly common problem in that era. As soon as is convenient for you, you should replace the fuseholder with an inline holder that accepts the flat automotive fuses (type ATC or mini-ATC).
This is available for only a couple bucks in the RV section of WalMart, or any hardware or big box store. Be sure to buy a box (probably 5) of replacement 30-amp fuses to fit this holder.
Please let us know what you find - everyone learns from the feedback.
Bill