Try replacing the power cord.

Your symptoms suggest a short circuit. (if your power supply checks out)
especially the part about kicking the stand.

it is probably where the cord plugs intot the back of the computer,
and when you
unplug/plug it makes contact again.

I would suggest replacing the power supply, cord and where the cord plugs into it. ( I think that's all included, but I've never replaced one)

Just my $0.02