Macbook startup problem

Hello,

I have a Macbook Pro (A1278) and I am having the problem this guy have: https://www.youtube.com/watch?v=u5H0SvvwxYw

If I keep the power button for a couple seconds after several tries it actually starts but everything is VERY slow.

The battery seems to have some problem because the message "Service battery" showed up a couple weeks ago. But I disconnected the battery and used only the power cord and it did the same.

When after more than 30' it was a little useable, I managed to check the disk utility and the S.M.A.R.T. status is verified.

Does anyone have any idea on what's the problem?

Thanks.