I had the same problem for quite a while with my N900. The N900 wasn't charging, and when I plugged it into the charger or USB cable, it would light up for a short while before going dark again. It would then restart and do this over and over. Had almost given up on it.

One important step helped me resolve the issue:
I bought a desktop charger on ebay for the BL-5J battery to charge it. This enabled me to charge just the battery (without the phone). I let it charge for a couple of hours.

I put the battery in the N900, and lo and behold, the phone didn't restart and it booted up. There was just enough charge for me to plug in my Nokia travel charger and charge the phone completely.

Apparently, once the battery is totally dead, the N900 can't boot into charging mode to charge itself. Bad design Nokia.