One of the the springs in the battery compartment of my Zoom H4 seems to have flattened and now the battery will not make contact to turn on the recorder: Anyone have the same issue?

SOURCE: Display reads "No Card"

Zoom h4 supports cards up to 2GB. And, I'm almost sure, this is a thing that can't be upgraded through software.

SOURCE: Mac OS 10.4.11 does not recognize the Zoom H4 recorder

Mac OS 10.4 and higher require the Zoom H4 to be upgraded. 
Go to  http://www.zoom.co.jp/english/download/software/h4.php#a  and choose the download to version 2.20 that applies to you. The instructions are there, but it is a little tricky. You must download the upgrade to your computer and then transfer it to your Zoom SD card.  To do that you need an SD card reader.  I used my digital camera. I took the SD card out of the zoom and put it in the digital camera. I Plugged the camera into the computer and when the SD card icon appeared on the desktop I dragged the "System Bin" file from the download to the zoom folder.  The rest of their instructions were pretty good.   Good Luck.

SOURCE: upload recordings from zoom h4 to ipod

if you are using a Mac running Leopard (Sys 10.5), you need to upgrade the H4  firmware from Zoom website
http://www.zoom.co.jp/english/download/software/h4.php

You will need an external SD card reader.
Once you do this, you can them plug in the Zoom to the mac with a usb cable, then select Connect to PC with the jog wheel.
The disc should show up on you desktop, and then you can download the files - (Should be in the folder marked STEREO)
Good Luck

SOURCE: Zoom H4 Battery Problem

I am having the same problem with my Zoom-H2. I have 2 2650 mah rechargeables, and the draw is such that 20-30 minutes of record &/or playback kills the batteries. Last night I just turned the power on and did nothing. 5 hours later the batteries were dead...

This isn't a solution. It is a reaffirmation that you aren't crazy!

SOURCE: zoom h4 Vista recording

Don't know if this is the problem in your case ... but here's what I did:
Note: I have Win XP
Previous to attempting connection between laptop and H4 as an audio interface I updated the H4 firmware to ver2.4 and connected to the laptop successfully as a card reader. From the laptop, I could see files I knew were on the H4 card.
... but when I tried connecting in Audio I/O mode, my laptop didn't know what to make of the H4. There was a USB mass storage driver associated with the H4 - I could see this from the "Device Manager". I "uninstalled" the USB driver associated to that "unknown" USB device. I terminated the audio connection on the H4, then reconnected. !!! It was recognized as "USB Audio Device" in the "Sound, video and game controllers" section of the "Device Manager". Before, it was listed under "Universal Serial Bus controllers" as a generic USB device with a yellow warning highlight indicating there was something wrong.
Hope this helps!