Is there a walk-around system I can purchase that would be compatible with the DC10
First, while I am not too familiar with the DC10, I have used the Aristo Train Engineer (TE) systems for years, and the latter expect a 12V-24V DC input. If you look at the small print on your DC10 it will probably say "Input xxVAC, Output 20VDC" or similar.
In other words, the DC10 is a standard railroad transformer and any throttle or walk-around system will work with it, as long as they are designed for the higher voltages associated with G-scale trains.
Checking the output of your DC10 is pretty easy - any multimeter or even a 24V bulb will tell you if it is producing the rated voltage.
That being said, you might want to take a close look at the Aristo TE. They are pretty robust and I know many layouts still using them after all these years. Two things to check - some versions of the TE receiver (RX) have a fuse clearly visible on the front. They also have a red LED that blinks when you push a button on the remote.
And finally, check the Aristo TE remote transmitter has a decent battery in it.
I googled "site:gscalecentral.net aristo train engineer" and got a lot of threads. Unless you are determined to junk it, I would suggest you glance at one or two.