The H4 most likely had software that allowed you to import your files directly into Cubase LE. Normally in your type of setup you can USB your tracks either directly to your computer or they have software that will convert the tracks into wav files that you can copy to your computer. You then take the .wav files and drag them into Cubase or use the import function in Cubase.
If connecting your H4 to your USB port makes it show up as a mass storage drive, and you can see the tracks as .wav files, or anything compatible to Cubase, you should be able to drag them directly into Cubase from the H4. I used to use the Fostex Mr16 in the same way. Fostex had their own software to download at their site, which exported the files from the MR16 to the computer and back, and would convert them into the appropriate format for each direction.