You might just start with the cheap $4 phone cord between the remote and inverter. While that is probably not the cure, it is the lowest cost way to rule that out.
You can write to this group, and they have lots of experience with Trace inverters and inverter/chargers.
HomePower.com My guess is that a new inverter/charger will be much lower cost than yours was 10 years ago. That will solve the problem for sure.
Check several locations, including SolarOnSale.com Amazon.com Sunelec.com and your favorite local solar dealership. Internet sales have a lot of competition, and prices are held pretty low as a result.
I have read some of the history of Trace inverters, the guy who bought several inverter companies creating Xantrax, and the history of Outback Inverters. My next inverter will probably be a Outback inverter. The guy who designed the Trace inverters has been working at Outback coming up with more innovative items, and making military grade inverters that are totally sealed, so that dust would not be a problem anymore!
Check HomePower.com Magazine for advertizes of this inverter. It will be much more durable than the Trace inverters, like the 1997 version that I have in my motorhome.
Good luck!
Fred.