Will not power on from ac or batteries

No solution, just a workaround. I have used the H2 with firmware 1.90 successfully with Windows 7, but lately the H2 is not recognized anymore. Built-in obsolescence maybe?
Anyway, I just take out the card and put it in a card reader. It is faster also. Card readers are cheap.

Most digital voice recorders, have a filing system. It is usaully labeled either: A, B, C, D or 1, 2, 3, 4 (these are the main folders) and each of these folders contains a set amount of files (in most cases about 99 subfolders). So you can have folder A file 1, 2, 3 and so on... When pressing the RECORD button for the first time you are in one of the main folders and your recording gets a sub folder number. To continue recording where you left off last time or where 'stopped' use the PAUSE and not the STOP function. The moment you press STOP instead of PAUSE you will change the sub folder number - and therefore not have one continous recording. If you turn the power off or remove the batteries you will also change the sub folder number. Most of the better recorders have a voice activation function that places the recorder on pause automatically when there are no sounds. It will not change the sub folder number when it starts recording again - and will automatically pick up where it left off.

I can't get any sound? What is the problem?

I have exact same problem, I got it to work temporarily by turning unit on then connecting AC adaptor into unit, it forced it to run, I formatted card and it worked for an hour now back to same old problem, I'll keep you informed. I believe it's faulty switch. help me if you can.

This implies that there is not enough current going to the device when running on battery (only back-light but no data) whereas running fine on AC means that the device board is most likely in a good operational condition.
I think maybe once a leaked worn battery which left forgotten inside battery compartment damaged the battery terminals or at least the wires connecting these terminals to the main board, i would recommend you to open and check on that.

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!

You have an IC (Integrated Circuit) that has shut off internally. Try complete power down (remove any electrical power - includes any internal batteries) overnight. Then try again. If this doesn't work, it's an IC malfunction.

How to Record:
1. Make sure HOLD switch (on side of unit with pocket clip) is set to off position (slide to right is off - to left would be hold)
2. For best results set unit with mic(rophone) which is on top of unit toward sound source and press REC/STOP button (Top button on front of unit just below LCD display). Recording will begin and will be indicated on LCD display.
> Red Record LED will be on and the message number, recording time will be displayed on the LCD.
3. To stop recording, press REC/STOP button one time.
* If no other buttons are pressed within 1 minute at stop position, it will power off automatically.
4. Pause during recording by simply pressing MODE/PAUSE button- press button again to resume.

There is a Voice Operated System (VOS) Recording button on left side also. You can record with voice activation to conserve recording space but I have found that you lose a portion of the recorded sound as it activates and if there is no sound for a very few minutes the unit powers off and you will get nothing further recorded. I recomend just keeping VOS in off position.

5. To erase a recording: Select the message number you want to erase and while it is stopped (the message number will appear in LCD with the length of recording showing also)
Press and hold the ERASE button until the LCD begins blinking "ERASE" then, while it's blinking simply press the erase button again and the recording will be erased.

6. To play back a recorded message find your message by "toggling" the switch on the right side of the unit that says INDEX. That switch is the fast forward/reverse play etc. To Play simply push the switch in. This button/switch takes a little practice to use but the Play portion is straight forward. Use the front buttons to pause and stop during playback.

Hope this helps.

I presume you have tried new batteries, and/or the problem persists with the AC adapter. If so, have you tried replacing the SD card?

If these do not work then it is probably time for a repair, but I'd ask the Zoom Corp or your dealer first. They may have heard of similar problems and know a painless fix.
www.zoom.co.jp (Japan)