Onkyo Push-Down Poke-In Ribbon Cable PCB Connectors

Think about replacing, if possible.
Flexible 10 way cables are sold are sold, and with plug and socket system, you will have to replace the socket, and solder a set of ribbon cables to the male plug, and make sure it cannot be reversed.

They are referred to as 'space shuttle' connection strips here, and are not as reliable as expected after about 10 years.
Basically a set of strips laminated to a flexible plastic material.
They were used for print head supply in dot matrix printers...if I see the picture correctly, it reduces in size if I try to increase it....!
And I remember those in CD drives as well, for the lens.
 
Variation is pitch and number of connections.
Another picture shows cables with end connectors which plug in, like SATA cables.

Do some work, we are not sitting around to babysit you.
Even after I complained about a poor picture, you did not post here, preferring to link to a picture sharing site.
Some enthusiasm is expected....
 
Molex 52004 series. I was looking to repair my HT-R391 with a new HDMI input board and thought these were plugs. Woopsie. Of course, these are long obsolete and I broke the cover. I think the wire can be removed by pressing on the cover; I pulled and broke the cover. I've found a few of them online however I have to buy a minimum of 10. I'll probably try to de-solder the connector and just solder the wires to the board. Called wire trap or push in connectors.