Black wire....

This is my now somewhat elderly R/C transmitter which was used a lot in the 1990's for both fixed wing and helicopters. I gave up model flying for various reasons in the latter part of that decade. However I decided several months ago to see if everything was still working but to my dismay (and possibly my fault) discovered that the back up battery had failed and that there is now some black wire disease!
I have a friend who has taken up the hobby and I thought I might join him but now the decision has to be made - do I get this repaired or see if I can afford new equipment and all the digital bits which are meant to be so much better. The other reason is that it could be fun for the grand children to have a car to play with under supervision when they visit. Well that's my excuse anyway........
What to do, which way to go - those are the questions.