Where can I get this type of connector from?

Is that a 4 or 5 pins connector? You can search for "4 pin connectors".

JST SH series maybe?

It's really hard to tell from the picture.

http://www.newark.com/jst-japan-solderless-terminals/shr-04v-s-b/wire-to-board-connector-receptacle/dp/33P8106

http://www.jst-mfg.com/product/pdf/eng/eSH.pdf

Could also be a Hirose connector.

Are there and logos or initials on it?

http://www.hirose-connectors.com/connectors/H205SeriesGaiyou.aspx?c1=DF13&c3=3

i'm with misterX it looks like a JST SH or H type

Have you tried pulling it at different angles? It might possibly even be soldered in.

check on the underside, normally there is a locking tab that must be pushed down to unlock and release

Definitely a JST SSH connector

To pull it out there is a tiny slot on the bottom side of the white part,

it is meant to be squeezed but I can never get it so I do this:

1 power off

2. insert a micro screwdriver flat blade in about .5 cm and pull slightly on white, and remove blade

3 brace the yellowed bit firmly

4 pull the white out at a slight angle towards the board, firmly and slowly

hope this helps

here is the data sheet:   http://www.jst-mfg.com/product/pdf/eng/eSH.pdf

For those types of connectors I don't like using my small screwdrivers; you can chew up the plastics pretty good.  I'd use a larger screwdriver, or better yet a plastic pry tool (aka spudger or black stick).  A lever motion to separate the male piece from the female piece causes considerably less strain than any pulling.  Just attack both sides evenly so as to avoid bending the pins.

I don't think that that is the correct one (which is an HR) , but it might be shown from the other side.

you are looking for an SH or SSH I believe.

If you are looking for an exact fit you will need the model number from the one on the board, 

I  think that , if you can solder , that it would be best to get town new mating units and redo the connection.

but in any case take the one out now and see if you can;t find some identifying numbers on it, that way you may be sure of the correct connection.

a lot of the plastic bodies are close, and not quite correct, for different manufacturers.