low-power conditions can be more dangerous than having too much power; the battery is the only saviour in a low-power situation.
Most electronic devices are required to state their power usage; I have a thinkpad myself and on the bottom below the type listing, it lists power usage of 16v 4.5A. The power supply itself should state on it what it supplies; it may list it in volts and watts instead of volts and amps (mine is in the back of a lot of stuff, I don't wanna try to dig it out atm) but that's just as useful. Remember - watts = volts * amps (or, watts/volts = amps, since that's what you might have). If the amps supplied by the power supply meet or exceed the amps desired by the laptop, then you've got the right power supply (too many amps is ok; you'll only draw what you need. Need exact volts though). Could be a bad powersupply though. If it charges fine elsewhere, the battery is almost certainly ok.
Simple test: remove the battery from the laptop, plug in the AC power supply, and see if the computer works. My thinkpad passes this test.
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