MacBook Pro 15" turn on itself when pluging power cord.

Good morning Apple users,

I have hère a MacBook Pro 15" mid-2012:

MacBook Pro 15"

Core i7 2,3 GHz

MacBookPro9.1

MD103F/A

This MacBook Pro has been left aside for one year. It wasn't supplied by power during this period. So, it wasn't in charge or discharge for a long while.

Here is the description of the symptom:

1. The MacBook Pro is off.

2. The MacBook Pro's screen is closed.

3. I plug the MacSafe power adapter.

4. I wait 1 or 2 seconds.

5. Suddenly, the MacBook Pro power on itself !

Same thing while the screen (step 2) is open.

Additional observation:

- The battery menu warn me the battery must be replaced now ! Same message in system profile and in the energy saver preference panel.

- Reseting PRAM, NVRAM and SMC (no matter the order) has no effect.

Question:

In my opinion the battery is dead.

But, is it normal that the MacBook Pro start up automatically just after I connect it to power supply ? Is this behavior a consequence of the fact that the battery is dead ?

In advance, thank you so much for your help !

I wish you all a lovely day !

TheUnknownMac

:-)