D and E drives are typically for the optical drive...odd that that would be the usb connector. (A is reserved for Floppy disk drives, C is hard drive, D is optical drive, E is occasionally a cd/rw drive on desktops, USB ports are the rest.
I don't have a PSP, but there probably some kind of software that proceeds connecting the device to the computer that you have installed on desktop but not laptop.
The drive letter itself is irrelevant of sorts - they don't require different drivers. If your computer is missing a USB driver, Dell has a site that gives drivers by computer model at
Dell Drivers and Downloads
Also, if one drive doesn't work, the vast majority of laptops have at least 2 usb drives - plug it in to a different physical port may work.