Hi Ken,
It looks like there's a difference in the way the two iPods function when power is applied/removed. Rather than trying to figure out how to get the new one to work the way you want, have you considered upgrading the hard drive in your original iPod to a bigger size, or even converting it to an SD card so you can put in any size you want?
I've got an old 20GB classic that I converted to take a micro SD card and now it's running a 128 GB flash chip. The conversion is exactly as difficult as simply replacing the drive; rather than putting in a new drive, you install an adapter that lets you plug in a flash memory chip of some sort, whether that's compact flash (CF), secure digital (SD) or trans flash (TF)/micro SD, it's only limited by the hard drive interface. On mine the maximum was 128 GB so that's the biggest I could use, but you'd have to do some homework to figure out what the max size of yours is. I don't know, but I'm guessing it'll be at least as big as the new drive you got, and possibly much larger.