The sector size on the new FAT32 drive could be too large for the Jensen. FAT32 standard allows a wide range of sector sizes (512 bytes to at least 4 KB) and clustering arrangements to support devices ranging from 2MB to 16TB. The computer writing to the larger storage device could very well format the device to use blocks and clusters not in the range of what an older client can handle.
I've run into this often on solid state storage devices for cameras, as capacity has progressed. Sometimes I've been able to make the camera reformat the storage media, in which case it might use half, or a quarter of the nominal capacity, but I doubt that your player has even that much smarts.