Suddenly slow Mac, not charging, and turning on takes ages

Hi, my Macbook Air suddenly stopped taking any charge in, as the light in the Magsafe port doesn’t turn on. I have tried cleaning both heads with a brush and alcohol, no result. Also, I have to keep the turn on button pressed for a long time in order for it to turn on. A short press will make the startup chime but the Mac turns off instantly when I stop pressing the key.

And finally, the computer takes several minutes to turn on completely, with Desktop showing. Before, it used to take around 30 secs. In general its very slow, opening light apps takes several minutes as well and the overall use is very laggy.

I have tinkered with Macs before but here I am helpless. Any idea what it could be?