Okay, so you replaced the MagSafe board, and now the charger LED is turning orange, which it wasn't before. That means that before, the electricity was not reaching the battery, either because the the MagSafe card was damaged, the logic board was damaged or the battery was dead. If you replace the MagSafe card and it changes, the MagSafe card was part of the problem. Now, what else happens as a result of that problem?
If the battery is drained, but the computer sees the battery and thinks it works, you may have to get it charged up a little before the laptop will start - even if it's on an AC charger. Leave the computer connected to the charger overnight; then check the battery sensor on the left side of the bottom case, and see if more than one of the charge LEDs light up.
It's probably also a good idea to reset the SMC controller before attempting your next start:
Reset the System Management Controller (SMC) on your Mac
Once you've done all that, try to power up your computer.
It's possible that the battery is dead, or nearly dead; it's five years old. Some laptops will run successfully with AC+dead battery, but there doesn't seem to be a consistent pattern. If your battery is having problems and you can't replace it immediately, you can try disconnecting the battery from the logic board and using the AC only, at least as an experiment.
For what it's worth, I used a 2008 MacBook Aluminum with a damaged battery circuit as my desktop system for several years. A liquid spill had damaged the logic board's power circuit, so it couldn't recognize any battery installed. It worked fine from AC only, but I had to be very careful moving the laptop around to avoid disconnecting the MagSafe plug.
Please report back with the results.