MacBook Pro 2009 doesn’t boot without charger

In my case, the problem was the temperature of the charger. Since it's currently winter in the southern hemisphere, removing the MacBook from charge causes the charger to cool down (since it apparently draws very little mains power when there is no load on the MacBook side). At some point when it is cool enough, it will refuse to supply power when the MacBook is plugged in again.

The workaround is to warm up the charger (for example, by sitting on it) for a few minutes until the charge light comes on. Then the current running through the charger is enough to keep it warm, and it continues charging.

Update: A year later, after returning from being away for six weeks, my charger refused to work again even after sitting on it. Apple was happy to replace it under AppleCare.

Yes - the SMC reset should resolve any temporary issues with the hardware not sensing the charge adapter. It's even called out in this KB article by Apple as something SMC reset can potentially address:

http://support.apple.com/kb/ht3964

Once you ruled out SMC needing to be reset, you should get the Mac in to a repair shop or do what they would do to isolate the hardware failure:

• test your adapter with another computer
• test your computer with another adapter
• test your computer with another OS (last resort - SMC and the charging behavior you report can be tested with the OS powered off and only the firmware / SMC regulating the LED color and charge state based on the data it can collect which is faulty in your case)

Once they have isolated the failure (likely to your computer), they would open it and inspect for any corrosion or damage on the logic board and charging circuitry and the either swap and test the magsafe board or the battery or the logic board itself based on experience and the hardware service manual for your model.