My X61 tablet lost the power light this morning. It was asleep plugged in and when I woke up I noticed the moon icon (Sleeping) lit but the plug icon (Charging) dark. I thought maybe it was the wall outlet, but no. The computer turned on but wouldn't charge. Examined the AC adapter, it seems fine but I noticed the transformer is not warming up even when left in the wall awhile. Not sure what the implies.

Maybe your battery died.
Does it start on AC without battery?

No the battery is fine. It starts on battery without AC. And it could run like that indefinitely were it infinitely charged. It doesn't receive power from the AC and so doesn't charge. And no, it does not run on AC without battery. I tried that. Again, the hardware green LED indicator lights: the plug light does not come on when AC plugged into wall and computer. The battery light comes on if I turn it on though, and if it's asleep the sleep light is lit normally.

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From your description, it could be several things and here's what's needed for verification:

- AC adapter is kaput; best way to determine (without endangering any other equipment) is to measure the voltage at the DC plug. Refer to the Hardware Maintenance Manual for proper procedure: http://download.lenovo.com/ibmdl/pub/pc ... 551_02.pdf If you don't have a voltmeter, an alternative is to try plugging the AC adapter into another 20V Thinkpad and see if it works there. Words of warning: If the AC adapter is putting out more than the 20V it is supposed to, you risk damage to the other laptop.
- AC outlet is dead; you said you "thought maybe it was the wall outlet, but no". Just to be clear, did you try plugging in a light or appliance into the same outlet and verify it's getting AC power or plug the AC adapter into another outlet you know works?
- Fuse is blown inside Thinkpad; assuming that the AC adapter and wall outlet are not the problem, then it's possible that the fuse that protects the DC input inside the laptop has blown. Only way to verify is to take the system apart and measure the fuse with an ohmmeter.
- Thinkpad's DC jack is broken; a very small possibility is that the DC jack inside the tablet is busted. That would prevent the 20V from being delivered to the motherboard.
- motherboard issue; something else besides the fuse and DC jack is causing the problem. This would mean changing out the motherboard as it's not too practical to troubleshoot and replace any individual parts on the board.