I am trying to use the H2 as an SD card reader via a USB connection, but the computer does not recognize the H2.
When you connect the H2 to the computer using a USB cable, the USB MODE SELECT screen appears, but the connection between H2 and computer is not yet in the online condition. Use the [REW]/[FF] keys to bring the cursor to "USB STORAGE" and then press the [REC] key. The H2 and the computer will then be in the online condition.
For details, see the section "Using the H2 as an SD card reader" on pages 71 - 73 of the operation manual.