Need to ID G4 part:socket came off logic board (blue & white power cable

Question

In the course of disassembling a G4 iBook the socket for the blue & white power cable wiring harness broke off the logic board.
I am trying to learn the correct desciption of this part so I can find a replacement. The wires on the bottom which were soldered to the board broke off.
Even after it was broken off, and I had leverage, I had to use two pairs of pliers to get the plug out of this socket. It should never have been assembled so tightly.

Answer 1

Spud-- I'm going to use conductive epoxy; I don't have access to anyone with micro soldering skills.
re previous posts -- unfortunately the Search logic is not precise enough to ask about this particular connector. Any search containing "logic board" gets swamped with the famous failure issue.
I went to an electronics specialty store and they didn't have any connectors of that style, let alone size. I'd like to replace the socket so I can use the existing plug on the blue & white wire.
Last night I spend some hours surfing "connector" etc and didn't see any photos that matched it on any distributor/manufacturer sites. So I'm still wondering what the correct descriptive word is, as used in the trade.
My "backup" iBook G3/Panther is taking about 30 seconds to load an average web page though. Spinner locks it up while loading one at a time. Wonder if installing Tiger and a newer Safari would help? I just got a chip to max out the memory, still have to install it.
For those who haven't seen it, the plug is a solid rectangle with two holes; the socket has a rectangular single cavity with two prongs sticking up from the bottom. TINY, THIN prongs.
The socket bottom has no leads on it (anymore). They are broken off flush with the plastic on the bottom. I was thinking of using a dental burr to grind into them, creating a small cavity, and then using conductive epoxy. I don't know if the bottom plastic is thick enough; if I go too far then it would ruin the prongs sticking up in the cavity.
But I could epoxy a wire stub, as long as possible to still fit into the space above the board & below the top of the shield/case. Then epoxy each wire to the pad on the board. The pads are about 1 mm x 2 mm or less, and worse, the gap between them is under 1mm wide. I'll have to goop some insulating silicone putty in that gap before putting tiny dabs of epoxy on the pads.
I bought some larger socket/plugs at the store, the socket part has no leads in it though. These sockets are they type that use the wire lead of the style shown in your photo of the repaired plug. I also got some different ones with flat prongs.
I'd like to move the connection point from the board to under the case top -- the blue & white wire runs all the way from the other side of the case. I just need a thin enough connector. Worst case -- leave as much slack wire length as possible and solder a Western Union splice.
If I can epoxy leads to the board without shorting between the pads I can figure something out. Need to carefully estimate the space available. Or as you say, just make some prongs.
You say #26 is the right wire gauge -- that's vital data. I don't want to undersize the power leads !
I'm also going to paint non-conductive coating on the board around the pad area, so I can slop the epoxy without worrying about shorting a trace. I've had to do some scraping to remove the gummy gluey stuff -- I presume its silicone adhesive of some kind.
There is some sort of test connection right above this area, with two little prongs sticking up. Marked "J1." The traces look like they go to the socket. I wonder if they use that to use alligator clips to power up the board during assembly testing? That location is much, much larger than the pads for the socket.