My 2012 MacBook Pro was starting up when power supply was plugged in. It had a bad battery, which I removed.
After removing the battery, it still started up when the power supply was plugged in, even after doing the system power management reset described above.
''Once I had a new battery installed, doing the reset worked.'' Apparently you need a working battery to do the reset.
***It's important to follow all of Danio1's steps. Note however:***
1. In step (A) - when I held the power button for 10 seconds the MBP turned on. I then shut it down again to go to step (B).
''* Make sure to shut down the MBP before you go to step (B).''
2. In step (B) the MBP does not do anything (no sound or lights) when you hold the four keys down.
3. ''Follow step (C), starting up, disconnecting the power supply, then shutting down the MBP.'' It doesn't sound like much, but I think unplugging the power supply causes the MBP to recognize that it has a battery installed and that it needs to manage the battery.
[The reset is more commonly called "SMC reset", for "System Management Controller".]
About having a bad battery:
# If the trackpad starts to get hard to click, the battery is swelling inside. You need to remove the battery ASAP. Note that lithium batteries, especially one which is swelling, are a fire risk. Handle with care if you remove it yourself. You will need a small "trilobe" screwdriver to remove the battery - that is, one three "arms", like a phillips head screwdriver, but with 3 edges instead of 4. This is in addition to a very small ("00" sized) phillips screwdriver to remove the bottom of the MBP. It's also a good idea to have something plastic (the corner of a credit card will work) to pry up the sides of the battery connector. iFixit has good tutorials on how to remove and replace a MBP battery.
# I've read that a 2012 MacBook Pro will run at about half-speed if the battery is removed. I didn't check this on mine.